.99999...=1

September 30, 2007 6:55 AM

No, I'm sorry, it does.There are some arguments that never end. John or Paul? "Another thing coming" or "Another think coming?" But none has the staying power of "Is 0.999999...., with the 9s repeating forever, equal to 1?" A high school math teacher takes on all doubters. Round 2. Round 3. Refutations of some popular "They're not equal" arguments. Refutations, round 2. You don't have to a mathematician to get in on the fun: .99999=1 discussed on a conspiracy theory website, an Ayn Rand website (where it is accused to violating the "law of identity"), and a World of Warcraft forum. But never, as far as I can tell, on MetaFilter.
posted by escabeche (256 comments total)

Neither exist.
posted by Henry C. Mabuse at 7:03 AM on September 30, 2007

This "controversy" annoys me to no end. Under the reals, yes. Under some other number systems which include infitesimals, no. Hooray!
posted by Arturus at 7:05 AM on September 30, 2007 [7 favorites has favorites]

NERRRRRRRRRRDDDDDDDDDDDDSSSSSSSSSSS!
posted by kittens for breakfast at 7:07 AM on September 30, 2007 [2 favorites has favorites]

"Another think coming"? What?
posted by washburn at 7:10 AM on September 30, 2007

JOHN.
THINK.
NOT EQUAL.

there, see? all you had to do was ask.
posted by quonsar at 7:10 AM on September 30, 2007

"Another think coming"? What?

it's very simple basic grammar.
"if you think x, you've got another think coming."

if you think it's "thing", you've got another think coming. "thing" in that sentence doesn't even make a whit of sense. you may as well say "toast" or "cheese" or "fencepost", for all intensive porpoises.
posted by quonsar at 7:15 AM on September 30, 2007 [4 favorites has favorites]

think? really? how does that even make sense?
posted by milestogo at 7:16 AM on September 30, 2007

"thing" in that sentence doesn't even make a whit of sense

saying "thing" means, "if [that is the thing] that you think [you are going to be getting], you've got another thing coming!"
posted by milestogo at 7:17 AM on September 30, 2007

I'm pretty sure that if you read the first references in print you'll see that the phrase originated as "another think coming." But whenever my parents used to say this to me as a kid I heard it as thing.
posted by Turtles all the way down at 7:18 AM on September 30, 2007

it's very simple basic grammar.
"if you think x, you've got another think coming."

quonsar is correct. "You've got another think coming" is the equivalent of "think again."
posted by amyms at 7:19 AM on September 30, 2007

.99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
is the loneliest number that you'll ever do.
posted by Falconetti at 7:19 AM on September 30, 2007 [11 favorites has favorites]

and yes, .99999...=1

1/3 + 1/3 + 1/3 = 1 is the simplest way for me to see it.
posted by milestogo at 7:20 AM on September 30, 2007 [5 favorites has favorites]

an Ayn Rand website (where it is accused to violating the "law of identity")

That link's a little disappointing. It's just a guy asking if it violates that "law", and a bunch of other people answering in typical ways (the typically right ways and the typically wrong ways).

I was hoping for "The government is behind this plot to make us think that .9999... is equal to 1. The IRS uses it in its calculations to steal even more of our money. One more benefit of an unbridled free market (as if we needed any more!) would be that this despotic and obvious violation of the Law of Identity would cease almost immediately."
posted by Flunkie at 7:20 AM on September 30, 2007 [4 favorites has favorites]

watt quonsar said.
posted by pompomtom at 7:21 AM on September 30, 2007

this problem is like a plane on a conveyor belt
posted by bhnyc at 7:22 AM on September 30, 2007 [3 favorites has favorites]

Watch out, quonsar, there's this huge think right behind you!
posted by sour cream at 7:23 AM on September 30, 2007 [2 favorites has favorites]

Under the reals, yes. Under some other number systems which include infitesimals, no.

Jesus, no. Even in nonstandard analysis, where you're messing around with infinitesimals, this infernal thing is equal to 1.

This isn't a deep mathematical fact - it is an unfortunate artifact of the decimal representation system, when you allow repeating representations. Any number with a "terminating" representation can also be represented with repeating 9's. Just take the rightmost nonzero digit, subtract 1, and drop on those fun repeating 9's.

Example: 1230 = 1229.9r

.9r and 1 are both standard real numbers. In nonstandard analysis, the difference between them can't be an infinitesimal, because the difference between any two real numbers is a real number, still. Infinitesimals are a huge red herring.
posted by TypographicalError at 7:23 AM on September 30, 2007 [5 favorites has favorites]

think? really? how does that even make sense?

It's a deliberate grammatical error, intended to be humorous.
posted by DevilsAdvocate at 7:24 AM on September 30, 2007

"another think coming" is just utterly retarded, nearly as bad as "for all intensive purposes". since when is think used as a noun by adults? plus a "k" just before a hard "c", that's just ugly in the mouth.
posted by nicolas léonard sadi carnot at 7:25 AM on September 30, 2007 [2 favorites has favorites]

My parents used to use that on me all the time. "If you think you can get away with that, young man, you've got another think coming!"

And it's "for all intents and purposes", not "intensive purposes". :)
posted by Malor at 7:26 AM on September 30, 2007

"another think coming" is just utterly retarded, nearly as bad as "for all intensive purposes".

Hmmmm? "You've got another think coming" has a clear meaning, regardless of whether you think it's grammatical or not. And that clear meaning matches the phrase's actual usage in context.

What does "another thing coming" mean? How does it match with usage?

since when is think used as a noun by adults?

Since (at least) the early 19th Century, according to the OED.

I'm not saying it wasn't used as a noun before that - I'm just saying that their example usages as a noun date back to 1835.

plus a "k" just before a hard "c", that's just ugly in the mouth.

Which is exactly why a lot of people think it's "thing".
posted by Flunkie at 7:31 AM on September 30, 2007 [2 favorites has favorites]

Language Log on the think/thing debate.
posted by monju_bosatsu at 7:32 AM on September 30, 2007

Wow, I feel like I put two really virulent bacteria together in a Petri dish and now I'm seeing which one is truly stronger. Good work, "thing vs. think."
posted by escabeche at 7:33 AM on September 30, 2007 [2 favorites has favorites]

No, the simplest way is:

1 - .99999999.... = .00000000... = 0

Therefore 1 + 0 = .99999999.......

Therefore 1 = .9999999......
posted by DU at 7:34 AM on September 30, 2007

In fact, I just happened to notice that one of the subentries for "think" as a noun in the OED actually is "to have another think coming: to be greatly mistaken."

Example usage listed there goes back to 1937. Here's one such example in the OED:

Any design consultant who thinks he is going to get British Leyland right by himself on his own has got another think coming.

Explain to me how "Any design consultant who thinks (such-and-such) has got another thing coming" makes more sense.
posted by Flunkie at 7:35 AM on September 30, 2007

If you define 0.999... as 1-(1/Infinity) then this all comes down to what you think the result of 1/Infinity is.

If you think dividing a number into infinite pieces results in no quantity, then 0.999... == 1. If you think you end up with infinitely many pieces then 0.999... <> 0.
posted by public at 7:36 AM on September 30, 2007

What the hell is happening on metafilter today? Revenge of the bad high school education?


.99999...=1

Don't focus on the 9's and the 1. The most important part of this is the "...".
posted by Pastabagel at 7:38 AM on September 30, 2007 [3 favorites has favorites]

Also, I had no idea there was a thing vs think controversy. How is it even a question that "thing" could be right? I mean...duh.
posted by DU at 7:40 AM on September 30, 2007

Merriam-Webster also has "think" as a noun, and also explicitly gives "another think coming" as an example.
posted by Flunkie at 7:42 AM on September 30, 2007

Good work, monju, but there's a newer LL post that has cites (with images of the actual newspaper stories) of "another think" from 1897 and 1898. You "think makes no sense!" people just aren't getting it. You're letting the fact that you learned the alternate form first cloud your understanding. And the process of making verbs and nouns out of each other is ancient and natural in English.
posted by languagehat at 7:45 AM on September 30, 2007 [3 favorites has favorites]

And of course 0.99999.... = 1. Didn't any of you unbelievers ever take a math course?
posted by languagehat at 7:45 AM on September 30, 2007

Okay, so then if zero can be equal to .000000000000..., is positive number x divided by zero = infinity?
posted by billysumday at 7:46 AM on September 30, 2007

Okay, so then if zero can be equal to .000000000000..., is positive number x divided by zero = infinity?

Yes.
posted by public at 7:49 AM on September 30, 2007 [1 favorite has favorites]

The WoW link is my favorite:

"There are two theories that math doctors use it is x=1 and true factor numbers. "

Wooo math doctors! *high-five escabeche with my true factor numbers*

Also, things like this:

If you define 0.999... as 1-(1/Infinity)

make about as much sense as saying "If you define 0.999... to be a smallish not-quite-ripe avocado, then this all comes down to what the best recipe for guacamole is." The answer is, nobody defines it to mean that, because that wouldn be silly.
posted by gleuschk at 7:50 AM on September 30, 2007 [4 favorites has favorites]

Okay, so then if zero can be equal to .000000000000..., is positive number x divided by zero = infinity?

Yes.

Really? Awesome. Then why is it taught as x/0 = zero?
posted by billysumday at 7:52 AM on September 30, 2007

Er, would.
posted by gleuschk at 7:52 AM on September 30, 2007

Okay, so then if zero can be equal to .000000000000..., is positive number x divided by zero = infinity?

No. Positive number x divided by zero is undefined.

The limit of a constant positive number x divided by positive number y, as y approaches zero, is infinite. But "x over zero" itself is not defined.
posted by Flunkie at 7:53 AM on September 30, 2007

Really? Awesome. Then why is it taught as x/0 = zero?

Whoever taught you this has another think coming.
posted by Flunkie at 7:54 AM on September 30, 2007 [16 favorites has favorites]

...

What is the sound of one hand waving dismissively?

...
posted by The Card Cheat at 7:57 AM on September 30, 2007 [2 favorites has favorites]

on think vs thing, it doesn't really matter which is the first usage, or which makes more objective sense - for mine is an aesthetic objection! "another think coming" is simply abominable. anyone who uses that form may as well be hooting and screeching like a barbary ape. i won't stand for it. i simply WON'T.
posted by nicolas léonard sadi carnot at 7:59 AM on September 30, 2007 [11 favorites has favorites]

Okay, so then if zero can be equal to .000000000000...

I'm not sure what this is supposed to say.

is positive number x divided by zero = infinity?

No. Division by zero just can't be given a sensible interpretation if you want the rules of arithmetic to continue to work.

Really? Awesome. Then why is it taught as x/0 = zero?

If you were taught this, you should ask for your money back.
posted by gleuschk at 7:59 AM on September 30, 2007 [5 favorites has favorites]

e^(i * pi) = -0.99999....
posted by neuron at 8:00 AM on September 30, 2007 [5 favorites has favorites]

on think vs thing, it doesn't really matter which is the first usage, or which makes more objective sense - for mine is an aesthetic objection!

Sure, now that your complaints about first usage ("since when is think used as a noun") and making objective sense ("it's as bad as 'for all intensive purposes'") have been shot down, yours is an aesthetic objection.
posted by Flunkie at 8:02 AM on September 30, 2007

If you were taught this, you should ask for your money back.

If I were to assemble the ways in which the state of Indiana deprived me of a proper education, I'd have 1-.9999999... time for anything else.
posted by billysumday at 8:02 AM on September 30, 2007 [1 favorite has favorites]

Explain to me how "Any design consultant who thinks (such-and-such) has got another thing coming" makes more sense.

Well, the "thing" coming is a realization, or a bad surprise or etc.. Heck, it could be a "think" if you think "think" can be used as a noun.

Also, one can have "another thing coming" even if one initially believes, or supposes or hopes, or etc., since using "thing" dispenses with the kind of past-its-expiration-date joke of using think as a noun.

Interestingly (well maybe...), these expressions don't seem to mean quite the same thing, since "another thing" tends to focus on the consequences that will force rethinking, while "another think" seems to suggest either that the thinker is in some humorous sense owed a rethinking, or simply that this person is likely to at some point rethink their position.
posted by washburn at 8:04 AM on September 30, 2007 [1 favorite has favorites]

TypographicalError: I didn't say that all number systems with infitesimals have .9r != 1, I said that some such systems existed. I was thinking in particular of the surreal numbers. The key is that if the number system you're working with is an extension rather than an alternative to the reals, then .9r = 1 will hold, because .9r and 1 continue to be valid reals, and all you've got is some extra things in there. Under the surreal numbers, as well as some other systems I'm less familar with, I'm sure, .9r and 1 are not real numbers, because there are no real numbers within the system. They exist entirely outside of the Reals.

So, I guess the inifitesimal is a bit of a red herring, in that it's not really the fundamental difference which makes it work, but it is a key part of the real-alternatives which makes it work. Wikipedia has a section of their article which talks about systems where .9r = 1 breaks, although it's not the best written.
posted by Arturus at 8:05 AM on September 30, 2007

make about as much sense as saying "If you define 0.999... to be a smallish not-quite-ripe avocado, then this all comes down to what the best recipe for guacamole is." The answer is, nobody defines it to mean that, because that wouldn be silly.

Why is it silly? Because it contradicts another rule of maths? Dividing numbers by Infinity is a perfectly sensible thing to do.

What is x/Inf? Some infinitely small quantity.

1/Inf < 2/Inf though.
posted by public at 8:05 AM on September 30, 2007

An esthetic objection is fine—I'm all for people using language in ways they find esthetically appealing. As long as you don't object to other people using language in ways they find esthetically appealing, of course.
posted by languagehat at 8:06 AM on September 30, 2007 [1 favorite has favorites]

A lot of confusion would go away if the arguement were prefaced by saying that 0.999... = 1, by definition - not by universal decree. They have equivalence within a defined number sysytem, if you want to define another number system, that's cool too. I really must get around to that one of these days.
posted by MetaMonkey at 8:06 AM on September 30, 2007

Well, the "thing" coming is a realization, or a bad surprise or etc.

And what other is the "another" in "another thing" referring to?

"another think" seems to suggest either that the thinker is in some humorous sense owed a rethinking

No, that's not true. It means that the thinker's thought is egregiously wrong.
posted by Flunkie at 8:07 AM on September 30, 2007

those are both aesthetic arguments! think as a noun sounds childish and "for all intensive purposes" crude; childishness and crudity uglify language; qeddy qed qed.
posted by nicolas léonard sadi carnot at 8:10 AM on September 30, 2007

How does "intensive purposes" sound "crude"?
posted by Flunkie at 8:13 AM on September 30, 2007

There's some trick where you can map it to an asymptotic function where the value at 1 is undefined and show that it exposes a contradiction in the notation system. That's all it is though, a bug in the way numbers are represented (double-naming) not a real mathematical paradox. Nothing to see here people, move along...

I remember getting into an argument with some guy on a forum about this ages ago. He didn't believe it was real, and his only argument was to repeat

"No! 0.99999.... doesn't equal 1, it's 0.99999....! TWO DIFFERENT THINGS ALTOGETHER!!!"

over and over and over.

I thought I'd serendipitously stumbled on a Turing Test for humans.
posted by L.P. Hatecraft at 8:16 AM on September 30, 2007 [1 favorite has favorites]

well, what the fuck is an intensive purpose? it's crude in its flabby imprecision.
posted by nicolas léonard sadi carnot at 8:17 AM on September 30, 2007

Let us not forget the important work of Downing, Halford, and Tipton in 1982.

If you think I'll sit around while you chip away my brain
Listen I ain't foolin' and you'd better think again
Out there is a fortune waitin' to be had
You think I'll let it go you're mad
You got another thing comin'.
posted by Remy at 8:17 AM on September 30, 2007 [5 favorites has favorites]

MetaMonkey more or less has it above, by the way. Here's the point:

Neither 0.99999.... nor 1 is a number. They are strings of characters. Obviously, they are not the same string of characters.

Over the centuries, mathematicians have developed a systematic way of assigning numerical values to strings of characters. It is not the only way of doing this you can imagine. For instance, you could decide "all strings of characters have the value 0." But this would not be very useful. The standard system of assigning values to strings of characters, on the other hand, has proven to be extremely useful. It conforms with our geometric intuition in many ways, it makes the process of adding and multiplying the values of two strings of characters relatively easy, etc. In this standard system, 0.99999.... is assigned the same value as 1. And the customary use of the equals sign in mathematics is to denote "these two strings of characters have equal values under the standard system of assignments," not "these two strings of characters are the same string of characters." So that, for instance, 1/2 = 0.5 is unobjectionable.

To sum up: If you ask "What IS 0.99999...." you have asked a question whose only reasonable answer is "a string of 11 characters." If you ask "What is the real number assigned to 0.99999.... by the standard system," then the answer is "1", or , more pedantically, "the same real number which is assigned to the string "1"."

Also, it is "think." But over the years I've become more tolerant on this matter to the point that I no longer ruin family dinners over it.
posted by escabeche at 8:18 AM on September 30, 2007 [11 favorites has favorites]

Also, positive x / 0 = +Inf and negative x / 0 = -Inf.
posted by public at 8:18 AM on September 30, 2007

I learned it as "you've got another thing coming", and I've been assuming that the "think" version was something created/encouraged by hasty internets typists. I'm fairly certain that I've never written it, and until recently, I've not seen it written often.

("Thing" makes perfect sense to me - it's generic and faintly menacing: think of some 40s gangster movie where a bad guy says to someone "You got away with it this time, but if you think you're gonna keep stealing from Mr. Big, you got another thing coming." "Thing", here, can be anything - a bullet, a beating, a pair of cement shoes and a cold lake. "Think" would be way wrong - is the henchman telling this other person that they should go away and think about what they've done? Not menacing at all, that.)

The "think" version just seems weird to me. Fortunately, I've managed to avoid writing it for a few decades now, so it won't be too hard to keep not writing it. I'll flinch when I see it written though, as I have in the past. And in this thread.

It's a mute point. *rimshot*
posted by rtha at 8:18 AM on September 30, 2007 [6 favorites has favorites]

Really? Awesome. Then why is it taught as x/0 = zero?
posted by billysumday

It's not. As any fule kno, x/0 is equal to null.

(No, not really. I know it's ridiculous, it's just a gag and an opportunity to use a Molesworth-ism :) )
posted by kaemaril at 8:20 AM on September 30, 2007

I'm with DU. I'm surprised that there is any controversy over the "another think coming" phrase. "I've always heard it wrong and don't feel like pronouncing the two words correctly" isn't really a compelling counterargument.

In fact, I always assumed that Judas Priest's "Another Thing Coming" was a witless wang reference. But it might actually be a whole different kind of stupid. That's worth noting, at least.
posted by ibmcginty at 8:20 AM on September 30, 2007

well, what the fuck is an intensive purpose? it's crude in its flabby imprecision.

That's not aesthetics. That's usage. You just said, a moment ago, you didn't care about whether it "makes objective sense" or not.

You're complaining about the sound of a "k" followed closely by the sound of a hard "c", remember.
posted by Flunkie at 8:20 AM on September 30, 2007

rtha - exactly what i wanted to say, but with far less spluttering.
posted by nicolas léonard sadi carnot at 8:21 AM on September 30, 2007

quonsar writes 'if you think it's "thing", you've got another think coming. "thing" in that sentence doesn't even make a whit of sense. '

I can see by the links that there's a genuine dispute about this. However, if I hadn't read them, I'd have said exactly the opposite.

Replace 'think' with 'believe' as they are functionally equivalent here. If you believe X, you've got another believe coming? That certainly makes no sense -- to me at least. It's like it mixes up two different tenses in the same sentence. To be grammatically correct, surely the expression would have to be 'If you think X, you've got another thought coming'

Whereas 'thing' being referred to is a fact, a belief, a concept, whatever. If you think X, you've got another thing coming (to set you straight about this subject). That makes much more sense to me. But I've never used either expression, so I don't have a dog in this fight.

As for the .9999 = 1 -- I've no idea. I never took a maths class.
posted by PeterMcDermott at 8:21 AM on September 30, 2007 [2 favorites has favorites]

Also, it would be cool if there were ASCII characters for each of the numerals 0-9 but with a dot over them, so you could represent recurring digits properly. What would be even more awesome would be if floating point numbers could actually store recurring digits properly, so you never end up with 0.999999... instead of 1 when you're doing convoluted spreadsheet calculations with accumulating round-off errors.
posted by L.P. Hatecraft at 8:21 AM on September 30, 2007

Dear Internet. If you don't understand mathematics, shut the hell up.
posted by Nelson at 8:21 AM on September 30, 2007 [6 favorites has favorites]

you don't think a usage seeming "crude" is an aesthetic complaint? there's more to the aesthetics of language than just phonics, though that's certainly important.
posted by nicolas léonard sadi carnot at 8:23 AM on September 30, 2007

you don't think a usage seeming "crude" is an aesthetic complaint?

In the sense that "k followed by c sounds bad" is an aesthetic complaint? No, certainly not.

Especially when you're additionally saying (in the "k-c" case that you're trying to compare your complaint to) that you don't care about objective meaning.
posted by Flunkie at 8:26 AM on September 30, 2007

Fucking prescriptivists.
posted by spaceman_spiff at 8:27 AM on September 30, 2007 [2 favorites has favorites]

To be grammatically correct, surely the expression would have to be 'If you think X, you've got another thought coming'

Except, as noted several times in this thread and elsewhere, "think" has been used as a noun for hundreds of years at least.

And, please. "You've got another think coming" is an informal figure of speech. Such things are often grammatically quirky, and it's silly to pretend otherwise.
posted by Flunkie at 8:29 AM on September 30, 2007

Oh, and the k-c thing only matters if you ignore the way spoken English doesn't put stops between words.
posted by spaceman_spiff at 8:31 AM on September 30, 2007

i guess the idea that i have is that any complaint that's consequent to a violation of some subjective sense of "right" is going to be aesthetic in nature. is that acceptable?

in this case we have the "crudity" of "for all intensive purposes" offending against my sense of how language hangs together. i'm not sure what to call that, exactly - my internal grammar? - but it's certainly a subjective basis, and so my complaint must be aesthetic, right?
posted by nicolas léonard sadi carnot at 8:35 AM on September 30, 2007

At times like this, I usually turn to the lyrics of Judas Priest songs for answers. Their 1982 hit "You've Got Another Thing Comin'" clearly illustrates that it's "thing" and not "think." And their unreleased acoustic number ".999... ≠ 1 You Crazy Bitch" settles the other big controversy in this thread.
posted by goatdog at 8:38 AM on September 30, 2007 [6 favorites has favorites]

in this case we have the "crudity" of "for all intensive purposes" offending against my sense of how language hangs together.

No, it offended your sense of objective meaning ("what the fuck is an intensive purpose?", you asked, when pressed to state how the phrase was aesthetically crude).

Contradicting your claim that, in the other example that you're trying to compare this "aesthetic objection" to, you didn't care about whether or not it made objective sense - you only cared about its aesthetics.

By which you meant, in that case, the fact that a k followed by a hard c is "just ugly in the mouth".

Get your story straight.
posted by Flunkie at 8:41 AM on September 30, 2007

For god's sake, why is it so hard to accept that "think" can function as a noun, i.e., "session of thinking"? In this colloquial usage, it's analogous to "cry," which we generally use as a verb but can be a noun, as in "I'm going to sit down and have myself a good cry [session of crying] over that."
posted by FelliniBlank at 8:42 AM on September 30, 2007

At times like this, I usually turn to the lyrics of Judas Priest songs for answers. Their 1982 hit "You've Got Another Thing Comin'" clearly illustrates that it's "thing" and not "think." And their unreleased acoustic number ".999... ≠ 1 You Crazy Bitch" settles the other big controversy in this thread.

Well, you might think that if you were a neophyte, but upon closer inspection, if you play ".999... ≠ 1 You Crazy Bitch" backwards, you will hear that:

It's "think", not "thing", we were making a scathing commentary on mishearings in langauge. And we were lying about the .9 repeating thing. Kill yourself! Kill yourself!

posted by Flunkie at 8:44 AM on September 30, 2007

PeterMcDermott: As is natural for humans, you've justified the version you learned and are comfortable with by ex post facto rationalizations. It is possible to break out of one's preconceptions and review an issue based on new information (such as the fact that the think version is attested earlier and makes sense in a way you hadn't thought of), but I realize it's difficult.
posted by languagehat at 8:44 AM on September 30, 2007

I have a few thinks on the think/thing controversy but I'm sure that I will have more thinks to think about. The main think that I would like to express though is that "another think coming" is a very stupid phrase. I can accept that it was used first, I just think it's stupid.

Explain to me how "Any design consultant who thinks (such-and-such) has got another thing coming" makes more sense.

How about: If you expect to get this (such-and-such) thing, you've got another thing coming.

Oh, and .999... = 1. There is no controversy here, only confusion.
posted by effwerd at 8:46 AM on September 30, 2007 [2 favorites has favorites]

I didn't even know there was a thing/think controversy - I had just always assumed typo whenever I saw think. After reading all the arguments, I think that I have to admit that I am wrong. Although I like the sound of thing better, and can justify it's use in much the same way others earlier in the thread have, think seems like it is the "right" word in the phrase. What this means is that since I won't be able to let myself say the wrong one anymore, but really really dislike the right one, I'll just have to cut the whole phrase out of my vocabulary.
posted by arcticwoman at 8:48 AM on September 30, 2007 [3 favorites has favorites]

I have a few thinks on the think/thing controversy but I'm sure that I will have more thinks to think about. The main think that I would like to express though is that "another think coming" is a very stupid phrase. I can accept that it was used first, I just think it's stupid.

Do you really not grasp that it's because it's not the version you learned that it sounds "stupid" to you? Can't you see that if you had learned it the way you had learned the other, that it would sound fine to you?
posted by languagehat at 8:49 AM on September 30, 2007

here's my vote for 'thing' and the gangsterish menace it affords.
posted by grubby at 8:50 AM on September 30, 2007 [1 favorite has favorites]

Mathematical theoreticals, that's where I'm a viking!
posted by Uther Bentrazor at 8:50 AM on September 30, 2007 [5 favorites has favorites]

How about: If you expect to get this (such-and-such) thing, you've got another thing coming.

You've retrofitted the sentence in an attempt to support your view, replacing "if you think" with "if you expect to get this thing".

The phrase isn't simply used in "if you think you're going to get such-and-such" cases. It's also used, for example, as "Young man, if you think I'm not aware of what you did last night, you've got another think coming."
posted by Flunkie at 8:51 AM on September 30, 2007

Man I just lost all respect for Quonsar. Another "think" coming? srsly? If someone said that to me I would punch them in the face.

And for the record, it is "She knows just what it takes to make a crow blush." NOT "And she knows just what it takes to make a pro blush" in the song Bette Davis Eyes.
posted by vronsky at 8:53 AM on September 30, 2007

Metafilter: another fencepost coming.
posted by notyou at 8:54 AM on September 30, 2007

I have never seen or heard "another think coming" until this thread.

This is baffling to me.
posted by Arturus at 8:55 AM on September 30, 2007

since when is think used as a noun by adults?

You need to have a bit of a think about that.
posted by jennydiski at 8:57 AM on September 30, 2007 [1 favorite has favorites]

that's not my sense of "objective meaning"! it's my fondness for precision, for elegant and efficient language. it's unquantifiable! subjective! a basis for aesthetic argument, not logical debate!

TO CLARIFY: when i brought up "objective meaning" far upthread, what i meant was that in deciding between "think" and "thing", it's possible to determine from the context of the phrase's deployment which is the more apt usage, and further, that i didn't give a fuck which it was.
posted by nicolas léonard sadi carnot at 8:57 AM on September 30, 2007

Oh, and it's completely idiomatic either way. Both sorts of rationalizations seem post hoc to me.
posted by Arturus at 8:57 AM on September 30, 2007

Sure.
posted by Flunkie at 8:58 AM on September 30, 2007

excellent point, jenny. i stand humbled and corrected.
posted by nicolas léonard sadi carnot at 8:58 AM on September 30, 2007

It's "another thing coming" because it sounds better! Since when do words need to make sense?
posted by wsp at 8:58 AM on September 30, 2007

Arcturus: Apologies for being snappy. Infinitesimals are often brought up in this argument in a very handwavy way that makes me see red. But you are correct.
posted by TypographicalError at 8:59 AM on September 30, 2007

Metafilter: a whole different kind of stupid.
posted by TheWhiteSkull at 8:59 AM on September 30, 2007 [2 favorites has favorites]

LanguageHat: I wasn't trying to justify it as there's clearly loads of precedents/precedence for the 'think' version -- even though it didn't make any instinctive sense to me. To be honest, I wasn't even aware that there was an issue about it until today. I was just trying to explain to quonsar why the version I'm familiar with makes sense to those of us who have heard it that way. In fact, my own interpretation of it seems almost identical to rtha's, so I'm obviously not alone in making sense out of it in this manner.

Seeing it as an arcane version of 'think again' though, removed any lingering doubts I might have had about the issue.

So. Precedents or precedence in this context? Or either?
posted by PeterMcDermott at 9:04 AM on September 30, 2007

Of course, while I agree that 0.99999r = 1, I think it's a good thing HRH The Queen has never read this. I dread to think of her saying "0.9999 recurring agrees with this mathematics fellow" :)

Also, I've always heard "to all intents and purposes" instead of "to all intensive purposes" and "another thing coming" instead of "another think coming". But I'm a crazy Brit, you know :)
posted by kaemaril at 9:06 AM on September 30, 2007

Replace 'think' with 'believe' as they are functionally equivalent here.

Nope. Believe already has a noun version: belief. "If you believe X, you've got another belief coming" works about as well as think, and lots better than thing.

posted by Kirth Gerson at 9:09 AM on September 30, 2007

Sleep! That's where I'm a Vikink!
posted by Flashman at 9:09 AM on September 30, 2007

If you wanted the expression to be more normal, you'd say, "If you think X, you've got another thought coming." That's pretty boring, though.
posted by Kirth Gerson at 9:13 AM on September 30, 2007

Speaking of math, was it René Descartes who said, "I thing, therefore I am"?
posted by weapons-grade pandemonium at 9:14 AM on September 30, 2007

RALPH WAS A REAL VIKING
posted by papakwanz at 9:16 AM on September 30, 2007

damn it flashman
posted by papakwanz at 9:17 AM on September 30, 2007

Man. Is this Pedant Weekend at Metafilter or something?

"Welcome to all our treasured pedant members. We've set up a few threads for you to participate in, so just sit back, relax, and nitpick the weekend away."
posted by A dead Quaker at 9:18 AM on September 30, 2007 [2 favorites has favorites]

plate of beans people... plate... of... beans.
posted by joeblough at 9:19 AM on September 30, 2007

A dead Quaker, as I explained in the other pedantry thread that I know about, I'm really just pedantic in the face of incorrect wannabe-pedantry.

If someone wants to say "you've got another thing coming", that's actually fine with me, and I won't complain one bit.

When, however, someone starts claiming that "you've got another thing coming" is correct, and that "you've got another think coming" is incorrect, that's when I start complaining.

Anyway, regarding "we've set up a few threads for you to participate in", I'm embarrassed to admit that I am interested. I know of this one and the "Pedants; or, you're doing it wrong" thread. Are there actually others?
posted by Flunkie at 9:23 AM on September 30, 2007

To those who prefer the low nutrition of simply mouth feel, you've got another thin coming.
posted by stirfry at 9:24 AM on September 30, 2007

"If you believe X, you've got another belief coming" works about as well as think, and lots better than thing.

My point was that the noun version of think isn't think, it's thought. Nobody says 'a think just popped into my head'.
posted by PeterMcDermott at 9:26 AM on September 30, 2007

So, besides in the phrase "another think coming" how often is think used as a noun anyway? As for anyone criticism the post-hoc explanation of how "another thing coming" makes sense: just because it's post-hoc doesn't change the fact that it also makes sense. And given that using 'think' as a noun seems quaint and old-fashioned I'll use the modern version in my day-to-day life(read: practically never because it's a dumb phrase anyway) while letting other people use whichever tired version they prefer.
posted by Green With You at 9:26 AM on September 30, 2007

To those who prefer the low nutrition of simply mouth feel, you've got another thin coming.

You've got another think, um, ing. Yes, that's it, you've got another thinking.
posted by Flunkie at 9:27 AM on September 30, 2007

Do you really not grasp that it's because it's not the version you learned that it sounds "stupid" to you?

I think "think" sounds stupid, and that is the way I learned it. So I avoid this idiom altogether. (On the other hand, I think "thing" sounds stupid also.)
posted by enn at 9:28 AM on September 30, 2007

Yikes. "Another think coming," "Intents and purposes," and you hold "tenets" NOT "tenants".

As far as invented phrases, spelling, and usage I'll totally land on the descriptivist side. These aren't mis-spellings or new inventions from usage however, they are simply the wrong word based on a mis-hearing or inaccurate transcript.

It's as plain as the difference between "your" and "you're" or "it's" and "its". One does not substitute for the other in text. The issue is that we rationalizing humans are excellent at building backstories as to why something must be true, even when it isn't. (Harder to do with "your" and "you're", but people try.)
posted by abulafa at 9:32 AM on September 30, 2007 [1 favorite has favorites]

Oh and I also blame Judas Priest for this controversy.
posted by abulafa at 9:33 AM on September 30, 2007

escabeche: "Here's the point: Neither 0.99999.... nor 1 is a number. They are strings of characters. Obviously, they are not the same string of characters."

Well, I guess I do buy that this is a way out, but I don't think I agree that it's the point. Let's call it the semiotic solution: drawing a distinction between the sign and the signified.

Here's why the semiotic solution is not completely satisfying to me: When it comes right down to it, I'm not all that sure that (the numbers signified by) 9 × 10^-200 and 9 × 10^-201 are different in any useful sense. (Note for later: there's plenty of wiggle room in that word 'useful'.) Given that the number of atoms in the universe is (let's say, roughly) 10⁸¹ and Planck's constant is roughly 10^-34, I just don't think I understand what it means for two quantities to differ by 10^-116, much less 10^-200.

So if we're going to posit that there are, out there, "things" called numbers, which we're describing with these strings of numerals, I've got to admit that I don't see how it's possible for any two of those things to differ by that small an amount. This argument, seems to me, leads irrevocably to a floating-point picture of the numerical universe, where there is in fact a unique smallest positive number, and anything of smaller absolute value is necessarily zero.

This renders the original problem, of evaluating 0.9999..., pretty much moot -- that ellipsis there is just holding space for 115 or so nines, not infinitely many.

So what kind of argument would hold water? I think (have thought for a long time now) that the only sensible solution has got to be a language-game interpretation, or some variant. Mathematics is a (collection of) game(s) played with symbols; like any game worth playing, there are rules. You may change the rules if you wish, but you must admit that by doing so you are now playing a different game. If everyone around you agrees on the game you're all playing, and you start spouting about infinitesimals and 1/∞, you're not winning the game; you're trying to play a different one, and looking a little foolish.

The best games are the ones whose rules don't contradict each other. ("If hit by a pitch, you may take your base; but first you are out and the other team gets two runs" would lead to a less-interesting version of baseball.) Deciding that we want to be able to do arithmetic is a perfectly good basis for the rulebook. Then, we could add whatever rules we wanted, as long as they made the game playable and we all agreed on them. One of the settled-on rules in the game of elementary mathematics is that the sum of an infinite series is the limit of its partial sums. From this, there's just nowhere else to go but 0.99999...=1.

Calling them "rules" opens you up to accusations of elitism, so perhaps you'd like to call them axioms instead. Sounds more neutral. Plus, they do differ from the usual common-language things we call rules. The main difference is that they're changeable by fiat. Nearly as important, though, is that if you don't know what rules you're playing by, you're not really playing. Ninety-nine point nine (nine nine har har) percent of the confusion about the 0.99999... problem arises from ignorance about rules that are even more basic than infinite series: What does it mean to say two numbers are equal? What does "and then keep going forever" mean? If two things are equal, and I perform the same operation on them, are the two results equal? If you're anything less than completely explicit about the answers to any of these, you're going to end up with a puddle of goo instead of mathematics.
posted by gleuschk at 9:34 AM on September 30, 2007 [6 favorites has favorites]

Green With You:

So, besides in the phrase "another think coming" how often is think used as a noun anyway?

Not often. But, so? And anyway, sometimes. From the OED:

• Let's have a cigar and a quiet think.
• My own private think is that he will execute another voluntary.
• The cobbler..dispenses his ‘think’..to all comers on all subjects.

Back to your post:

As for anyone criticism the post-hoc explanation of how "another thing coming" makes sense: just because it's post-hoc doesn't change the fact that it also makes sense.

First: I didn't say it didn't make sense. I asked for how it made more sense. I asked this of people who were saying things like "'another think coming' is utterly retarded".

Second, it makes sense in some situations in which the phrase is used. Specifically, in cases like "if you think you are going to get such-and-such" or "if you think such-and-such will result".

These are not, however, the only situations in which the phrase is used. Again, an irate mother to her child: "Young man, if you think I'm not aware of what you did last night, you've got another think coming."
posted by Flunkie at 9:36 AM on September 30, 2007

PMD: Check your unabridged: a "think" is not the same thing as a "thought" -- it means "The act or an instance of deliberate or extended thinking; a meditation."

There really isn't another English word for the concept.
posted by lupus_yonderboy at 9:40 AM on September 30, 2007 [1 favorite has favorites]

Warning: The Content in this Article May be Inaccurate
posted by you at 9:41 AM on September 30, 2007

lupus_yonderboy:

Check your unabridged: a "think" is not the same thing as a "thought" -- it means "The act or an instance of deliberate or extended thinking; a meditation."

Oxford English Dictionary, "think (noun)" definition 2a:

What one thinks about something; an opinion.

posted by Flunkie at 9:43 AM on September 30, 2007

as i remember from geometry class, where we studied proofs (which is actually LOGIC, but thats the way they do it here in the states), .999...=1 BUT 1.999... DoesNotEqual 2 and neither does 2.9999=3. and etc.
apparently it only works for .999...
go figure.
but i forget why, exactly.
posted by sexyrobot at 9:43 AM on September 30, 2007

Do you really not grasp that it's because it's not the version you learned that it sounds "stupid" to you? Can't you see that if you had learned it the way you had learned the other, that it would sound fine to you?

No, because I don't think it's stupid because of what I'm accustomed to, I think it's stupid because it uses "think" as a noun in such a ham-fisted attempt at being clever.
posted by effwerd at 9:45 AM on September 30, 2007 [1 favorite has favorites]

where we studied proofs (which is actually LOGIC, but thats the way they do it here in the states), .999...=1 BUT 1.999... DoesNotEqual 2 and neither does 2.9999=3. and etc.
apparently it only works for .999...
go figure.
but i forget why, exactly.

The reason that you forget why, exactly, is because it's completely false.

1.9999... is 2. 2.9999... is 3. 45.78252999... is 45.78253.

What is 1 + 0.999...?

It's 1.999....

But 0.999... is 1, so 1 + 0.999... is 1 + 1.

Which is 2.

So 1.9999... is 2.
posted by Flunkie at 9:49 AM on September 30, 2007 [1 favorite has favorites]

Check your unabridged.

Unabridged? Playboy's Party Jokes has always said "unabashed." What do bridges have to do with anything? That makes no sense to me.
posted by Turtles all the way down at 9:53 AM on September 30, 2007

All you lunatics who want it to be "another think coming," you better think (think) think about what you're trying to do to me.
Yeah, think (think, think), let your mind go, let yourself be free.
posted by vronsky at 9:53 AM on September 30, 2007

* Let's have a cigar and a quiet think.
* My own private think is that he will execute another voluntary.
* The cobbler..dispenses his ‘think’..to all comers on all subjects.

The last two of these are surely obsolete uses. I've never in my life heard the word 'think' used in this manner.

The first use though, also offered up by jennidiski upthread, I think is confusing to me because it appears to be describing an action, and as such, so you inevitably think of it as a verb rather than a verbal noun.
posted by PeterMcDermott at 9:56 AM on September 30, 2007

Oh, LanguageHat. Given the citations, I know, in my head, that you are right. But my heart says otherwise. I never heard "think" used in this expression until the last year or so. It's always been "thing" in my household.

The focus is on "thing" not the verb. You want/think/expect one THING; you're going to get another. Usually presented in a rather threatening way, I'd say.
posted by etaoin at 9:58 AM on September 30, 2007 [1 favorite has favorites]

Flunkie,

Anyway, regarding "we've set up a few threads for you to participate in", I'm embarrassed to admit that I am interested. I know of this one and the "Pedants; or, you're doing it wrong" thread. Are there actually others?

We've also got the airplane on a conveyer belt thread for physics-minded bean plate overthinkers.

Just to be clear, I don't have a problem with all this--it amuses me. It's like a freaking pedant honeypot here.
posted by A dead Quaker at 9:58 AM on September 30, 2007

The last two of these are surely obsolete uses. I've never in my life heard the word 'think' used in this manner.

Yes you have. You just thought the person was saying "thing".
posted by Flunkie at 9:58 AM on September 30, 2007 [1 favorite has favorites]

The focus is on "thing" not the verb. You want/think/expect one THING; you're going to get another.

Again, the phrase is most commonly used following "if you think".

Sometimes it's "if you think you'll get a thing".

Not always.

This argument of yours is common, but it's really just based on pretending that a specific usage of the phrase is the only usage of the phrase.
posted by Flunkie at 10:02 AM on September 30, 2007

A dead Quaker, thanks!
posted by Flunkie at 10:03 AM on September 30, 2007

Just because the current common saying isn't the original doesn't make it wrong.

The saying "Another think coming" is the original usage and makes sense perfect if 'think' is used as a noun. This is probably the only time in modern usage that 'think' is used as a noun and so even if someone says "think" many people here "thing" which isn't a problem because...

The saying "Another thing coming" is a newer usage and makes perfect sense. It is in common usage and even has a song named after it. Some people don't like it probably for the same reason they don't like it when people say "begs the question" instead of "raises the question".
posted by Green With You at 10:08 AM on September 30, 2007

Well, you know, if .999 and .999999 and 1 were the same as each other, there'd be no need for all three, would there?

So, no.
posted by paperpete at 10:09 AM on September 30, 2007

I missed Flunkie's reply on preview and concede that some people use the phrase "another think coming" in very specific situations that make more sense than "another thing coming".
posted by Green With You at 10:11 AM on September 30, 2007

If you, like me, are interested in wasting some time, you might have a look at the Googlebooks results for "another think coming." It takes off in the early twentieth century as a joke, and H.L. Menken cites it as an example of American linguistic resourcefulness in The American Language (1921).

Those who point out that "another think" precedes "another thing" as an idiomatic expression are right. In the early part twentieth century, the phrase was familiar as a humorous expression.

On the other hand, these early uses of "another think" are humorous and non-standard, and dependent on the fact that "another thing" would have been standard English.

The example seems to provide an instance where a humorous idiom arises as a witty variation of everyday speech, and then slowly changes into a somewhat more standard expression as either 1) the original joke loses its punch over time, 2) casual speakers fail to notice the joke, or 3) a new and perhaps ironic usage arises that refers to the ominous "thing" that's lurking in the wings and waiting to surprise some poor sucker unaware. This last sense is observable in some of the comments here.

Interesting to consider.
posted by washburn at 10:11 AM on September 30, 2007 [5 favorites has favorites]

Flunkie, I yield the point! I've gone from believing people who thought "think" was right were insane to just maybe, possibly, perhaps they have a point and I'll rethink my resistance to it.

I'll start listening more carefully. While we're at it, what about this debate?

Newsday cover story headline ignites grammar war


Newsday
So is it "a" or "an"?

Dozens of readers called and many others e-mailed Newsday to complain about Sunday's Page 1 headline, "How An LI Nursing Home Empire Got Its Way." The story detailed a dispute between 12 indicted nurses and their former employer.

Most of the concerned readers argued that the paper had violated proper English usage by placing "an" before a consonant.

Newsday's editors, who consistently put "an" before "LI" in headlines, called the usage proper. Editor John Mancini called it "commonly accepted newspaper style."
....

It turns out the dispute hinges on just what the mind's ear hears when reading "LI," the common abbreviation for Long Island.

"This is actually a usage point with two defensible positions," said Bryan Garner, author of "A Dictionary of Modern American Usage." Like the AP Stylebook, his writing manual states that a word's sound - rather than its first letter - controls which indefinite article it takes. Thus, we write "a European country," "a one-year term," "an FBI agent" and "an MBA degree."

"It's perfectly defensible to say 'an' if the view is that people would say 'LI,'" Garner said.

Not everyone reads "LI" the same way, however.

"But if the view is that most people are reading LI as 'Long Island,' and that's what they're supplying in their mind, then they're going to want the word 'a.'"

posted by etaoin at 10:14 AM on September 30, 2007

Okay (oll korrect), I'll do it:

Metafilter: A freaking pedant honeypot
posted by Turtles all the way down at 10:26 AM on September 30, 2007

I missed Flunkie's reply on preview and concede that some people use the phrase "another think coming" in very specific situations that make more sense than "another thing coming".

You've got that exactly backwards.

There are very specific situations in which "thing" makes sense.

"Think" makes sense in all situations.
posted by Flunkie at 10:28 AM on September 30, 2007

Except, as noted several times in this thread and elsewhere, "think" has been used as a noun for hundreds of years at least.

Does that mean that LOLCATS will become standart english in a century or so?
posted by Zemat at 10:38 AM on September 30, 2007

To me, "another think coming" sounds like a Pogo-style malapropism, not wrong, exactly, just particular to a dialect.

Of course, until this thread I would have casually assumed that .9r < 1 by an infinitely small amount. Again a particularity.
posted by wobh at 10:39 AM on September 30, 2007

lol @ "Another think coming".

That is truly the product of mental retardation.


It's as annoying as the people who say "anyways".
posted by wfc123 at 10:42 AM on September 30, 2007

There are very specific situations in which "thing" makes sense.

"Think" makes sense in all situations.

Funny enough, I think you've got it backwards. All thinks are things but not all things are thinks.
posted by effwerd at 10:47 AM on September 30, 2007 [2 favorites has favorites]

Funny enough, I think you've got it backwards. All thinks are things but not all things are thinks.

Did I say that all things are thinks?

I said that in all situations where the phrase in question is used, "think" makes sense.

"Thing" makes sense in some of those situations.
posted by Flunkie at 10:50 AM on September 30, 2007

The decimal expansion problem (if you think there is a problem) arises not only with all integers, but with all rational fractions whose denominators contain only factors of 2 and 5. For example, 1/5 = .2 = .1999999.... This is because 2 and 5 are the prime factors of the arbitrarily chosen base of our number system. If we choose 7 as our base, say, 1/5 loses its vestigal decimal tail, because it can now only be represented as a non-terminating decimal, and they are pinned instead only on fractions whose denominator is a power of 7, in addition to the integers.

So if you believe .9999... does not equal 1, you are forced also to believe that infinite numbers of these entities wink in and out of existence merely as we vary our choice of a base to represent numbers-- a highly unsatisfactory and counter-intuitive state of affairs, since we ordinarily take for granted that changing the base does not change the nature of numbers in any significant way, if at all.
posted by jamjam at 10:54 AM on September 30, 2007 [1 favorite has favorites]

1. I dunno... George?
2. THING! THING! THING! Christ, are you people playing some sort of a prank? OED and Websters mention this phrase explicitly when saying that "think" can be a noun? Maybe that's because that's the only time ever that anybody uses "think" as a noun, and the only reason they do that is because they misheard the phrase as a kid and kept repeating it the wrong way. You are incorrect. OED and Webster have capitulated in the greater fight, but not I.

...jesus christ... "I have another think coming..."

3. Seems like mathematically, due to our number system, .99999... = 1. Conceptually, they are infinitesimally different. We're discussing two different matters.
posted by Navelgazer at 10:54 AM on September 30, 2007

And ralph dreams of being a viking.
posted by Navelgazer at 10:54 AM on September 30, 2007

re: the think/thing controversy I don't think either one makes any sense if you analyse them so the whole thing over which is the correct one becomes a moot point, and if you think it does matter then you've got another thing coming.
posted by electricinca at 10:59 AM on September 30, 2007

Oh and 0.9 recurring does so equal 1.
posted by electricinca at 11:00 AM on September 30, 2007

I could care less about the whole thing.
posted by Opposite George at 11:01 AM on September 30, 2007

Man I just lost all respect for Quonsar. Another "think" coming?

for all intensive purposes, you are damaging my self of steam.
posted by quonsar at 11:02 AM on September 30, 2007 [4 favorites has favorites]

"My self of steam" is just superb; the best along that line I can remember seeing.
posted by jamjam at 11:09 AM on September 30, 2007

Did I say that all things are thinks?

No, what I'm saying is that if all thinks are things, then any instance where "think" can be correctly applied, "thing" can also be applied. The assertion that "think" is applicable in all cases (of the example) but "thing" only in some cases is backwards.
posted by effwerd at 11:10 AM on September 30, 2007

"My self of steam" is just superb

i saw it on a high school girls website in a spiel about "bitchiz" who pretend to be bi to attract guys. linked on blort a long time ago.
posted by quonsar at 11:12 AM on September 30, 2007

The simplest explanation of 0.999... = 1 that I found convincing was: If 0.999... is not equal to 1, then there must be an infinite number of real numbers between them.

But one cannot write, construct, or conceive of even one, of course.
posted by Western Infidels at 11:12 AM on September 30, 2007 [2 favorites has favorites]

Yikes (Part 2).

Just because you believe a phrase sounds "right" doesn't mean its history is moot. Archaic, sure, but then so is "tenets" in all but philosophical circles, but that doesn't allow "holding tenants" to replace "holding tenets" as in "believing things".

Oh and washburn, I don't think you were trying to be dishonest but the search you used to illustrate "another thing" loses the context. Change the search thusly and you will see exactly zero instances of the construct under discussion in the first few pages.

Of course, are you trying to illustrate that in the 80+ years since the first instance in 1835 this same debate took place and the smarty-pantses of the early 20th century seized on it or are you trying to say that it's always been a joke? I don't think I can buy that.

Oh and regarding the original post, jamjam ftw. Totally clear and compelling separation of representation versus value.
posted by abulafa at 11:21 AM on September 30, 2007

No, wfc123, *your* usage is the annoying one. Just because you think something is stupid doesn't mean it is.

Please note that the "think" partisans are using the actual history of usage of the phrase and logic to back up their position. The "think" partisans are saying "it doesn't sound right" and using a specific example that just happens to fit their position ("if you think you'll get this thing..."), when the phrase is used in many other ways as well for which "thing" makes no logical sense.

You can say whatever you like, they sound close enough that people probably won't notice anyway. But don't run around saying that people who understand the original meaning and how it came about are "retarded."
posted by lackutrol at 11:25 AM on September 30, 2007 [1 favorite has favorites]

vronsky: And for the record, it is "She knows just what it takes to make a crow blush." NOT "And she knows just what it takes to make a pro blush" in the song Bette Davis Eyes.

I'm just going to assume you're trying to be funny, because it actually is "make a pro blush".


And it's "another thing coming". Washburn explains it best above. Yes, perhaps originally people made a play on "another thing coming" by punning "think"- but doesn't that suggest that "thing" was the true, original usage being punned on?

Flunkie's making this point unintentionally: the justification that "think" is some how a broader application is completely backwards, as effward points out repeatedly. "Thing" is a word in English that beautiful is a variable, allowing the speaker to use it as a placeholder for a usually context based object.

Yes, in any phrase that's "If you think X, then you've got another think coming", think is a perfectly meaningful usage. But thing is also perfectly meaningful, and has the benefit that any sentence structured without the "If you think X" also works with thing- whereas think would not really work that well.

I can't believe even people like languagehat are getting this wrong, and how ironic in a thread originally about .999... = 1. Since .999... = 1 only is confusing if you mistake the sign for the underlying meaning or value, and don't understand that they are effectively describing the same thing through different notation... then I guess you'd be the kind of person who thinks language is about following rules, as opposed to ensuring communication. If anyone says "you've got another thing coming", there's no English language speaker who fails to get the meaning involved. Even if the phrase jars them because they graduated from the Beanplate College of Pedantry, these Thinkites understand that "you are mistaken in your belief of X, and are sure to be perhaps unpleasantly surprised when future occurrences demonstrate that your original belief was incorrect!" is what is being communicated. Whereas in 2007, using "another think coming" at this point might be so weird as to distract the listener from even focusing on your content.

Conclusion: using "another think coming" disrupts communication, while "another thing coming" ensures communication. QED.
posted by hincandenza at 11:36 AM on September 30, 2007 [4 favorites has favorites]

Whereas in 2007, using "another think coming" at this point might be so weird as to distract the listener from even focusing on your content.

I guess it might be. But what this thread, and every other thread on every other forum about this topic, amply proves is that there are lots of people for whom "another think coming" is the actual phrase. And lots of people for whom "another thing coming" is the actual phrase. It seems to be a roughly even split. And among each of these groups, lots of people who have gone their whole lives without realizing that not everyone else is saying the same thing they are.

But it seems to be an empirical fact that both usages are widely used, and that this has been the case for a long time. And that either one, used in conversation, is going to convey the desired message without creating confusion. Even though "another thing coming" sounds ridiculous and ungrammatical to me, I'm sure people have said it to me many times without disrupting our communication -- because I thought they were saying "another think"!
posted by escabeche at 11:47 AM on September 30, 2007

Oh, puh-huh-huh-leeze.

Yes, anytime you use a noun, you could have used "thing" instead. I'm not debating that.

But the actual argument that pro-"another thing coming" people make is that the "thing" referred to is "something that you expect to get".

This includes effwerd, who got into this by saying "If you expect to get this (such-and-such) thing, you've got another thing coming", and only later pulled out this silly "all nouns can be replaced by thing" argument after his original argument was shot down.

And why was it shot down? Because it ignores the fact that the phrase is used in situations about "thinking", and not just in situations about "thinking that you are going to get something".

But yeah, all nouns can be replaced by "thing". Fantastic. And true. And a flatly absurd attempt at framing the pro-"another thing coming" people's actual argument.
posted by Flunkie at 11:48 AM on September 30, 2007

abulafa, I'm not entirely sure what you're saying in your post; however one thing to keep in mind is that Google Books does a very poor and confusing job presenting and sorting bibliographic information. Items that appear on Google with a date in the 1800's are often really things that were printed much later, but appeared in journals that were established in the 1800's.

I think you might be citing some twentieth century uses of "another think coming" as nineteenth century examples; however, again, I'm not quite sure that I'm understanding everything you've written in your comment.
posted by washburn at 11:50 AM on September 30, 2007

hincandenza: ...in 2007, using "another think coming" at this point might be so weird as to distract the listener from even focusing on your content. Conclusion: using "another think coming" disrupts communication, while "another thing coming" ensures communication. QED.

I'd never heard of the "thing" variant of this phrase before today. I find it so weird that it distracts me from the content. I find that it disrupts communication. Whatever is more common today, whatever the true origin of the phrase, your argument only works if everyone is just like you. And we're not.
posted by Western Infidels at 11:52 AM on September 30, 2007

and soon, if i have my way, you'll burn for it.
posted by nicolas léonard sadi carnot at 11:54 AM on September 30, 2007

effwerd, what? You seem to be saying that because "think" is used as a noun in this case, "thing" can always be substituted for "think" and make sense. So any noun can always be replaced by "thing" and make sense? Yes, nouns are things. What of it?

Can we try working this out with some examples?

"Jim, if you think you're going to get away with stealing my stapler, you've got another ______ coming."

"Thing" in this instance would be what? A box of doughnuts? A punch in the face? Another stapler? A thought?

"Think" would just mean that he is going to have to change his opinion ("think," here) shortly.

"Jim, if you think that you just ate pork, you've got another _______ coming...in fact it was cat."

"Thing" here would be what? A vomiting session? A reluctant realization about the arbitrariness of his culinary choices? The need for Pepto Bismol?

"Think" would just mean that he is going to have to change his opinion ("think," here) shortly, in this case when he is told he has eaten cat's meat.

Are you "thing" people just saying that the speaker can never think of the correct word for what he is referring to?
posted by lackutrol at 12:03 PM on September 30, 2007 [3 favorites has favorites]

If you believe that, you need to re-think since you're wrong.
posted by stirfry at 12:04 PM on September 30, 2007

washburn: Your example search regarding "another thing" searched for exactly that phrase, which doesn't really capture the context of this discussion, "another thing coming", and when I corrected that part of your search the results that came back never mentioned the phrase in the context under discussion here, "another thing coming".

All I did was take your searches (1900-1930) and change them to (1800-1900), retaining "another think coming" and "another thing coming" respectively to illustrate that the exact phrase, in the context under discussion "another think coming" appears often in the 1800-1900 searches whereas "another thing coming" does not appear at all in the first several pages I looked through for the same timeframe.

If you're saying the mechanism Google Books uses to determine date of usage (as opposed to publication or origin) is in question, then why use it to illustrate your original point?

My conclusion is that while this same debate may have come up in your 1900-1930 timeframe, that doesn't mean that we can assume that the 80 years of usage (from the OED cite above) are washed away by the fact that it had even then grown to appear archaic or at least unfamiliar and therefore ridiculous.
posted by abulafa at 12:07 PM on September 30, 2007

Another think coming
@Common Errors in English, which I consider the authority on these sort of things.
posted by BlackLeotardFront at 12:11 PM on September 30, 2007 [1 favorite has favorites]

If you think that's the authority on these sort of things, you've got another think coming.
posted by RogerB at 12:18 PM on September 30, 2007

BlackLeotardFront, a snopes-style cite or history would go a long way to making me believe that Paul Brians didn't cut his research short around the 1930's as mentioned above.

On a cursory inspection, I can't find any other item in his list I specifically disagree with, though.
posted by abulafa at 12:22 PM on September 30, 2007

But yeah, all nouns can be replaced by "thing". Fantastic. And true. And a flatly absurd attempt at framing the pro-"another thing coming" people's actual argument.

I don't think this is getting across: I am not arguing in favor of "another thing coming." The counter-example I brought up was to show applicability of the phrase "another thing coming" as it can be applied to expressing the concept of "If you expect X, that may not be the case." I did not realize at the time that this was an argument exclusively regarding the applicability of "another think coming" as it applies to only those cases where "think" is the preceding verb in order to satisfy the historical precedents of the phrase.
posted by effwerd at 12:23 PM on September 30, 2007

You're arguing that (you were arguing that) if someone uses "expect to get something" instead "think you're going to get something", then "you've got another thing coming" makes sense but "you've got another think coming" does not?

What if they just use "expect" instead of "think"? No "you're going to get something" involved?
posted by Flunkie at 12:38 PM on September 30, 2007

abulafa, I'm afraid I can only point out again that you're making a mistake in using Googlebooks to trace "another think coming" back until 1835 (or 1820, even?). You need to look more carefully at the title pages and citation information of the items you cite. I'm kind of surprised you didn't do this after I first pointed this out.

Looking at Googlebooks (which I'm not saying is a comprehensive method) suggests that the phrase is recorded as an idiom in the early twentieth century. Previous uses of "another thing coming" or "another thing" are just ordinary language and don't call for or receive any special attention. Then, in the early c20, "another think coming" appears, and is witty and jokey. Then, by the later c20 "another thing coming" exists as an expression, and is also a little strange, still retaining the ghost of the joke, as it were, from its early uses as recorded by Menken and others. As I said earlier, this is sort of interesting.

In any case, please do look a bit more carefully at the evidence you've been citing to show that "another think coming" had a lengthy pre-twentieth century existence.
posted by washburn at 12:45 PM on September 30, 2007

It's clear the "another think coming" argument was concocted to elicit outrage and attention.

It was a rousing success, yes. But pretty infantile, if you ask me.

The .99999 = 1 thing sounds ridiculous to me, but at least that argument could actually sway me.
posted by wfc123 at 12:50 PM on September 30, 2007

I thing I've figured this think out:

Use whichever one you want. Since it is an idiomatic expression, either is correct.

THE END
NEXT THREAD PLS
posted by papakwanz at 12:54 PM on September 30, 2007

Washburn, really, I started with your searches. The only thing I changed was the phrase in quotes, in that I corrected it to look not for "thing coming" and "think coming" but rather "another thing coming" and "another think coming". When that didn't corroborate your earlier assertion, I leveraged your research approach by changing the dates from 1900-1935 to 1800-1900.

While, certainly, I've now spent more time discussing the mechanism than it would have taken to read the content, I still don't understand how using the same mechanism you did save for changing the terms to something more relevant is so bankrupt in comparison.

In short: are you really saying that the presence or absence of "thing coming" and "think coming" between 1900 and 1930 (as Google Books calculates it) relates to this discussion? If you are then please explain how, as those phrases are necessary but not sufficient to represent the full phrase under discussion.

And why would you cite Google Books in the first place if they are such a questionable source? (Not that I disagree; I wanted to use the same source you did so we had a common basis for comparison, not because I think they're especially sensible.)
posted by abulafa at 1:04 PM on September 30, 2007

You're arguing that (you were arguing that) if someone uses "expect to get something" instead "think you're going to get something", then "you've got another thing coming" makes sense but "you've got another think coming" does not?

No. As I said, I am not arguing in favor of "another thing coming." I'm not even arguing against the fact that "think" is applicable in all cases of the phrase's usage. Trading "expect" for "think" doesn't change anything since all expectations are thinks, and the meaning of the phrase depends on expectations. I just thought that framing the argument as "think" applies in all cases while "thing" only applies to a limited set of cases was incorrect.
posted by effwerd at 1:04 PM on September 30, 2007

END OF ARGUMENT
posted by wfc123 at 1:05 PM on September 30, 2007

Not all that complicated. Suppose we call 0.9999999... "x".

Now surely, 10x = 9.99999999.....

10x - x = 9.9999999... - 0.99999999.... = 9 (exactly).

so 9x = 9

Therefore, x = 1.
posted by RichAromas at 1:11 PM on September 30, 2007 [3 favorites has favorites]

I'm not even arguing against the fact that "think" is applicable in all cases of the phrase's usage.

(...)

I just thought that framing the argument as "think" applies in all cases while "thing" only applies to a limited set of cases was incorrect.

I'm just not following.

You're not arguing against the fact that "think" is applicable in all cases, but you are arguing that the argument that "think" is applicable in all cases is incorrect?
posted by Flunkie at 1:40 PM on September 30, 2007

The conjunction is there for a reason.
posted by effwerd at 1:54 PM on September 30, 2007

All that this thread has proven to me (on the actual, mathematical front) is that our number system doesn't allow for a simple expression of the infinitesimal. That doesn't mean that it doesn't exist, or isn't useful. Hell, as far as I know (and acrtual mathematicians/coders are gong to prove me wrong here, I'm sure) there's no way for a Binary system to express fractions at all, as a simple number. That doesn't mean that 101/1000 (Binary for 5/8) doesn't exist as a concept, but that binary can't express it more simply. Similarly 1/∞ is the only way that our decimal system can express the infinitesimal, but just because we can't express it as a simple number, doesn't mean that it doesn't exist.

I find the point about how there must be "infinite numbers" between .99999... and 1 if .99999... ≠ 1 compelling, but again it's either the fault of imagination or our number system, and not that the concept doesn't exist as truth.

Just because you can't conceivably count to infinity doesn't mean that infinity can't work as a mathematical concept. It can and does. So does the infinitesimal have a place as a concept, even if, with our current way of playing with our symbols designed to represent to purely abstract, it becomes highly unwieldy.
posted by Navelgazer at 1:57 PM on September 30, 2007

Note: I was using "simple" there to mean, I guess, the inverse of "irrational," i.e. a number that can only be expressed as a fraction, or result of another mathematical formula (like 1-.99999...). I'm not a mathematician, so I don't know your terms of art. I apologize if I came off confusing/simply dumb in my comment above.
posted by Navelgazer at 2:01 PM on September 30, 2007

This is ugly.. instead of saying "we define it as such" they say "it is equal..". And then they complain that people don't agree with it. If I keep cooking pancakes for an infinite amount of time, how many pancakes will I have? Well, the question is when? Oh, you mean *after* you've been cooking for an infinite time? But there's no after if it was infinite, or else it wouldn't be infinite, right? So, don't try to sidetrack me, just answer if I will have infinite pancakes or just a large number, say a trillion, and if you say a large number then i will ask how large and then I win because I will show that it can't be that number no matter how large. I've read through that thread and nobody seems to understand that they're arguing about the wrong part.

Actually i've read about this a year ago on wikipedia and the only explanation that made sense of the argument is that some people see it as a process and others see it as an abstraction of an end of process.

So, I am of the opinion that .999.. is not 1. I see .999.. as a process that is undefined. If you expressly say that .999.. is something that will get to 1 after an infinity of adding if there was such a thing as "after an infinity", then I will agree, except that the other side does not like such kludgy definitions.

I think people who say .999.. == 1 are not wrong, they are just assholes. And they are not right either, they are just sloppy in their definitions.
posted by rainy at 2:09 PM on September 30, 2007

Time was that we didn't have a way of expressing zero, but that didn't mean that people didn't understand "nothing." Now, people can understand "infinitesimal" (though it's decidedly a more difficult concept) but we can;t express it.

But, of course, as soon as we developed the decimal system, math became perfect.

So it must be the concept which is wrong.

Bullshit.

When you use a man-made system designed to represent fundamental facts of the universe, and then the system can be used to declare the truth of something fundamentally untrue, then the problem is with the system, not with the fundamentals.

.99999... ≠ 1. It doesn't matter how you do your proofs. Your proofs are based in a system which can't recognize the infinitesimal, and as such are worthless in dealing with this issue.

As for thing/think, I'm willing to just say now that it's an idiom that no one really uses anymore and just let it be. Though I'm still pretty sure "thing" is right and "think" horribly, horribly wrong.
posted by Navelgazer at 2:27 PM on September 30, 2007

Hey, pancake boy. Cut one of those pancakes into three pieces. Take one piece. Now you have one third of a pancake, or exactly .3333... of a pancake. It ain't a process. It's a third of a pancake. If you have three of those you have .9999... pancakes, also known as one pancake.
posted by found missing at 2:28 PM on September 30, 2007 [2 favorites has favorites]

Once again, I'll ask. If you don't understand mathematics, then shut the hell up.

So when you say "as far as I know (and acrtual mathematicians/coders are gong to prove me wrong here, I'm sure", that's your cue to shut the hell up about mathematics.

And when you say "I am of the opinion that .999.. is not 1", that word "opinion" is your cue to shut the hell up.

Mathematics isn't about feelings and opinions and "as far as I know". It's a very careful, precisely defined formal logic system. You may not like it, but arguments about .9999.... not being 1.0 are about as coherent as an astrologer trying to convince an astronomer that they don't understand the motion of Mars.

(And Navelgazer, I think what you're actually trying to talk about is what's represented by ε when doing limits.)
posted by Nelson at 2:44 PM on September 30, 2007 [4 favorites has favorites]

The conjunction is there for a reason.

What, "while"?

So, then:

I just thought that framing the argument as "think" applies in all cases while "thing" only applies to a limited set of cases was incorrect.

But:

I'm not even arguing against the fact that "think" is applicable in all cases of the phrase's usage.

So you're saying "saying x while y is incorrect", but not "saying x is incorrect"?

So you're saying "saying y is incorrect"?

So you are arguing this silly "all nouns can be replaced by 'thing'" position?

Honestly, help me out here.
posted by Flunkie at 2:45 PM on September 30, 2007

Dear people who are flinging around "assholes" and "bullshit", but who have no idea what they are talking about:

You have no idea what you are talking about. You may express whatever opinion flies into your skull and rattles around in there, but it is not an informed opinion. As such, it contributes nothing. It's the equivalent of kibitzing on a chess game and saying "Hey, you should jump that one! Then you could get kinged!"

rainy: "So, I am of the opinion that .999.. is not 1. I see .999.. as a process that is undefined. "

You may hold that opinion. It is not an informed opinion, and is just as useful for the problem at hand as deciding that avocados are red instead of green.

Navelgazer: ".99999... ≠ 1. It doesn't matter how you do your proofs. Your proofs are based in a system which can't recognize the infinitesimal, and as such are worthless in dealing with this issue."

You may hold that opinion. It is not an informed opinion, and is just as useful for the problem at hand as saying LALALALALA with your fingers in your ears.
posted by gleuschk at 2:47 PM on September 30, 2007

Isn't it really obvious that the phrase was "If that's what you think, you've got another think coming," and the second think is a deliberately incorrect play on "thing?" Doesn't that seem pretty clear? And people have "corrected" it since its original use?
posted by BlackLeotardFront at 2:48 PM on September 30, 2007

Isn't it really obvious that the phrase was "If that's what you think, you've got another think coming," and the second think is a deliberately incorrect play on "thing?" Doesn't that seem pretty clear? And people have "corrected" it since its original use?

No.
posted by ibmcginty at 2:55 PM on September 30, 2007

gleuschk: I;m not expressing an opinion on this mater. I'm expressing a fact.

.999... ≠ 1. Fact

We no tgis to be true from common sense, though that doesn't prove anything.

However, I'm not putting my fingers in my ears and yelling LALALALALA. I'm telling you that your "proofs" on the matter are like the fundamentalists who started the flat-earth society. We know they're wrong., but they will refuse to listen to reason because "the bible" says this, if interpreted in such a way.

You system of math - not math itself, but our current representation of it - is flawed in this slight way. This is fact. The system is ever so slightly imperfect. Someday, someone smarter than any of us here will figure out a way to solve that, and their system will eventually be proven slightly imperfect as well, and so on.

Man-made representation of the basis of the universe continues to evolve, and isn't airtight as it stands. Stop saying that "the bible says it's so" bullshit and know that we don't understand how to perfectly represent everything yet. We never will, but we'll get closer as long as people can understand that sometimes the system needs improvement, when it testifies to something clearly incorrect.
posted by Navelgazer at 3:02 PM on September 30, 2007

Holy crap, that's ignorant.
posted by found missing at 3:03 PM on September 30, 2007

.999... ≠ 1. Fact

What does ".999..." mean to you?
posted by Flunkie at 3:05 PM on September 30, 2007

I feel 1.0 - 0.999.... is like a precious little flower. With the boot of fundamentalist mathematics stamping on its face. Forever.
posted by Nelson at 3:13 PM on September 30, 2007 [2 favorites has favorites]

To put it in another way - quantum physics doesn't jibe with Newtonian physics. Doesn't mean that Newtonian phyiscs isn't useful - in almost all cases it still "works" if by "works" we mean "expresses and predicts the nature of the universe." Geocentric theory is great for navigating ones way across an ocean.

The fact that our system is based on the number of fingers we have doesn't make it infallible, no matter how much we've been able to do with it. Astronomers stuck with Ptolemy for ages, because they could just keep refining their "crystal spheres" to more accurately reflect the motions of the heavens. When our decimal system requires that certain numbers can only be represented by fractions, or by pi, or what have you, we're just adding crystal spheres because none of us have the innate understanding of a different way to represent the math of the universe which might be better than what we've got.

Biting the bullet when the decimal system tells us something patently untrue, however, and then saying it must be true because the system says it, is ignorant fundamentalism. It's like when people are learn about Schroedinger's Cat, and then take away from it that, whoa, cool, the cat's both alive and dead at the same time! GO science.

No, the cat's either alive or dead. Schroedinger was giving us a paradox to show that while the math works, our representation of the universe doesn't trump that actual nature of the universe.
posted by Navelgazer at 3:15 PM on September 30, 2007

I'm quoting SCIENCE!
posted by found missing at 3:17 PM on September 30, 2007

To put it in another way - quantum physics doesn't jibe with Newtonian physics.

Fascinating. But again, when you say ".999... ≠ 1. Fact", what exactly is it that ".999..." means to you?
posted by Flunkie at 3:18 PM on September 30, 2007

It means, to express it using a system that has trouble expressing it, 1- (1/∞).
posted by Navelgazer at 3:27 PM on September 30, 2007

Isn't it really obvious that the phrase was "If that's what you think, you've got another think coming," ... And people have "corrected" it since its original use?

Yes, but the problem is that people who learned "thing" and didn't realize it was a misunderstanding of the original form get very defensive and instead of saying "Gosh, now I realize my version is a secondary development—I'll keep using it anyway because it's what I'm used to, but it's nice to know the history!" say "NO NO NO IT'S THING YOU'RE WRONG NOW SHUT UP."

Navelgazer: You really, really have no idea what you're talking about, and multiparagraph elaborations of your misunderstanding of mathematics are just digging yourself a deeper whole. You might as well be arguing that pi = 3.
posted by languagehat at 3:27 PM on September 30, 2007

It also means Christmas and the smell of a newborn baby.
posted by Navelgazer at 3:27 PM on September 30, 2007

"My self of steam" is just superb

i saw it on a high school girls website in a spiel about "bitchiz" who pretend to be bi to attract guys. linked on blort a long time
ago.

I'm sorry you don't get to claim it, quonsar (except the discovery of it, for which I am really grateful) but it's more wonderful as a naive production than it would be if it had been invented as a deliberate joke.
posted by jamjam at 3:30 PM on September 30, 2007

I'm quoting SCIENCE! posted by: foundmissing

It was my understanding of science that when it reaches a conclusion which is inherently paradoxical, it's time for a new paradigm, and not to simply say that the paradox is itself truth and stop there.
posted by Navelgazer at 3:34 PM on September 30, 2007

It means, to express it using a system that has trouble expressing it, 1- (1/∞)

OK. There's your problem:

That's not what it means to mathematicians.
posted by Flunkie at 3:36 PM on September 30, 2007

gleuschk: I think the “language game” interpretation is basically what was historically called the formalist position on the foundations of mathematics: that fundamentally, mathematics is formal manipulation of symbols according to definite rules, and anything else is non-mathematical. I agree this position resolves the question of .999... = 1, once the formal system is specified, but it avoids the harder question, “why this particular formal system?”

The real number system we use has been abstracted and formalized from intuitions that most people have about continuous lengths and how to quantify them in terms of fractions. And I would argue that any formal system conforming to these intuitions will also say .999... = 1, as long as the digits and = have the same intuitive meaning. If you assume otherwise, it quickly leads to unintuitive results, as others have pointed out in this thread. (On preview: I think you agree with this.)

You contrast the formalist position with a “semiotic” interpretation where the mathematical symbols are supposed to refer to some real thing. I guess this is similar to what was historically called the Platonist position, except that you are arguing against it based on what is physically realizable — whereas a Platonist would say that a mathematical object like a function exists in some ideal sense, not tied to physical reality.

First of all, I agree that a direct measurement yielding 10^-116 is hard to imagine, but there are any number of ways to construct quantities that small. For example, there are about (10⁸¹)² = 10¹⁶² possible pairs of particles in the observable universe. (Or if you want to get really big, there are about 2^{10^81} possible sets of particles.) We can talk about fractions of these possibilities: n distinct pairs of particles is n × 10^-162 of all possible pairs. I'm not arguing that this is a useful number, but at least it's concrete. In particular, we can compare any two such fractions (by comparing the numbers of distinct pairs in the numerator) — so here is a case where it's perfectly meaningful for two numbers two differ by 10^-162.

Furthermore, the usual way to formalize the intuition that measurements don't have infinite precision is with probability theory. The problem with simply using 115-digit floating point numbers is that uncertainty accumulates: the sum or product of two uncertain numbers is more uncertain than the originals. To quantify this uncertainty, we replace each uncertain number by a distribution over all its possible values. Which means, not only do we still need real numbers, but now we need functions from reals to reals (and all the machinery of analysis to manipulate them). Functions like “the normal distribution with mean 1 and standard deviation 10^-116” are even more abstract and less physically realizable than real numbers, and yet they allow us to answer useful questions about the uncertainty of measurements.

Navelgazer: you are right that the actual nature of the universe trumps the formal system, when it comes to interpreting mathematical results. However, you can't complain that the decimal system doesn't represent the infinitesimal, when you can't point to an example of the infinitesimal. “One over infinity” is not an example — it's a string of symbols representing a meaningless operation.
posted by mubba at 3:45 PM on September 30, 2007 [1 favorite has favorites]

"another thing" and "intensive purposes" are what you get when you let stupid people play with language.
posted by coriolisdave at 3:47 PM on September 30, 2007 [2 favorites has favorites]

Okay... I'm going to, well, not concede my point, but conceded that most people on this thread are atl east far more knowledgeable about formal mathematics than I am.

flunkie: please, then, explain what it means to mathematicians if not that. I think it's clear that there's something I must be missing here.

mubba: Why is 1/∞ a meaningless operation? Honestly, I don't understand. And if it is, indeed, meaningless, doesn't that only add weight to my statement that the decimal system can't represent the infinitesimal?

languagehat: Just don't even go there. I'm not a math-wizard, but this doesn't take advanced calculus to understand the subject here. I'm happy to admit that I don't know all the terms that might be applicable, but that doesn't mean that I don't know what I'm talking about. We're looking at a paradox, and people are embracing the paradox because the math works. I'm saying that the math that we're using is a system we ourselves have designed, and that the problem probably rests there.

Honestly, though, if there's something I'm obviously not understanding, please let me know. If nothing else, it'll help me sleep a little better and not feel so much like an asshole for debating smart people on unfamiliar ground.
posted by Navelgazer at 3:57 PM on September 30, 2007

please, then, explain what it means to mathematicians if not that. I think it's clear that there's something I must be missing here.

It's the sum of 9/(10^X) for every positive integer value of X.
posted by Flunkie at 4:23 PM on September 30, 2007

Navelgazer: 1/∞ is meaningless because ∞ is not a number. The symbol ∞ is merely a convenient notation for several different situations that suggest “a number larger than any given number.”

And actually, you are right, the decimal system does not represent the infinitesimal. However, without being able to point to a real example of the infinitesimal, that doesn't seem like a flaw (never mind a refutation of .999... = 1).
posted by mubba at 4:41 PM on September 30, 2007

Although you are very wrong, Navelgazer (in my opinion), you are wrong in a thoughtful and interesting way; if you continue to push forward in the direction you seem to be heading until you reach some answers you find satisfying, I am convinced you will be even more interesting-- and whatever you do understand, you will really own it and be able to use it.

If I were a teacher of yours, I would try to get you to take a look at the history of imaginary numbers. As with these repeating decimal things, they were controversial and their existence seemed to be implied by notational conventions and equations, but unlike the decimal things, you could make some powerful and beautiful new mathematics with them. The decimal things lead nowhere.
posted by jamjam at 4:49 PM on September 30, 2007

I have to admit, my initial thought was "but 0.9r is a number infinitely smaller than 1!" then I realised I just broke 0.3r= 1/3, and chalked it up to the awkward way we handle decimal fractions and infinity with real numbers. Compared to the weird shit I learned to live with in multivariable calculus for my engineering maths...

Oh, and intensive purposes? Gah.

"The correct phrase is "to all intents and purposes." This phrase dates back to the 1500s and originated in English law, where it was "to all intents, constructions, and purposes." In modern usage, "for all intents and purposes" is also acceptable. The phrase means "for all practical purposes" and is generally used to compare two nonidentical acts or deeds, i.e., "She went to his room and drank with him, which he viewed for all intents and purposes as consent to sex." A shorter equivalent phrase is "in effect."

I assume it's like which witch and they're, their, there. Sometimes I think english should just be taken into a back room and beaten senseless for needlessly confusing people. Don't get me started on bough, though, through, tough, borough, cough...
posted by ArkhanJG at 5:00 PM on September 30, 2007

Navelgazer: Sorry if I was too brusque and dismissive—that can happen around here—but it really is hard for me to see how anyone who knows anything about math (I'm not talking advanced calculus) can take the position you're taking. I mean, math is nothing without proofs. How do you deal with the proofs given above (for instance, 1/3 + 1/3 + 1/3)? Maybe I don't understand your point, but it sounds to me like you're just stubbornly insisting that you don't like the idea that 1 = 0.99999..., and, well, that just doesn't fly.
posted by languagehat at 5:02 PM on September 30, 2007

I'd also like a quiet word, with a big stick, with the people that decided Leigh Road is pronounced Lie (as in lie down) Road, Newbury Gardens is Newberry Gardens and Iwerne Minster is pronounced Youwern Minster.
posted by ArkhanJG at 5:13 PM on September 30, 2007

You "think makes no sense!" people just aren't getting it.

Oh, none of you people are getting it. Look:

1. It is likely that the phrase originated as "you've got another think coming", as a mild joke, swapping the verb to a noun;

2. It is undeniable that, for many English speakers "think coming" is awkward at best, and so unlikely to be pronounced correctly...leading to a common mispronunciation of the phrase as "thing coming";

3. The "thing coming" phrasing removes the mild joke, but does not remove the meaning from the phrase (as everyone continues to understand what you mean);

4. "thing coming" becomes the slang term in those regions where the local dialect makes "think coming" the most awkward, and "think coming" becomes the slang term in those regions where the local dialect supports that pronunciation.

YOU'RE BOTH RIGHT. Now eat your beans.
posted by davejay at 5:52 PM on September 30, 2007

Why is 1/∞ a meaningless operation?

Math forum: infinity is a concept that can't be used with operators.
posted by Brian B. at 6:09 PM on September 30, 2007

So the thing is, if I think a think is a thing I say "think" but if I think think ain't a thing I say "thing?"

I'm either smarter or dumber than I was an hour ago.

And how about people who say "we've got to flush out that idea" instead of "flesh out?"
posted by Bookhouse at 6:16 PM on September 30, 2007

Language- it differs between groups, and it evolves. Linguiphiles, I thought that was part of the fascination and study. I'm not giving carte blanche to hordes o shitty texters or all out bad grammar, but idiomatic expressions? Really? I appreciate the clarification, as well as the history lesson (being a 'thing' man myself), but if someone ever took the time to correct me, I think I'd punch them.
posted by potch at 7:44 PM on September 30, 2007

Okay, thank you all, I think I understand a little bit more now...

Moving from there, the point I'm trying to make is that the infinite and infinitesimal exist as coherent concepts, and I believe that a mathematical system should be able to work with them, much in the way that the ancient systems had to be redesigned in order to work with the concept of zero. I'm a liberal arts guy (actually a film student, now law student, but it all adds up to the same) and so I'm looking more at preserving the concept of the infinite and infinitesimal, particularly the infinitesimal, because the concept of it has always fascinated me (how many angels can dance on the head of a pin and all that.)

Let me put it this way, and this might be foolhardy, but disregarding the actual answer to the ongoing debate here...

if .99999... = 0, then there exists a problem with the system, in that two uniquely valued numbers are, in fact, not unique at all. This is a systemic problem.

if .99999... ≠ 0, but mathematical proofs make it seem so, then there is a problem with the math whereby it can be used properly to prove the untrue. This would also be a systemic problem.

Either way, the system is flawed, albeit in a rather unimportant way, but is still imperfect. This is to be expected of any man-made system of representation. I simply don't think we do ourselves any favors by embracing a paradox because we have so much faith in a man-made system as to believe it to be flawless.

I look at this debate as not being about whether .99999 = 0 or not. To me, there's no question that it doesn't actually. But I can understand the accuracy of the proofs. The real, underlying question is, is there a mathematical concept of the infinitesimal? And theoretically, yes, there is. Expressibly, as a function, no. The problem is thus systemic. That's why I've been so hard-headed here. Math and science evolve, and society follows in suit. We haven't reached the end of how we build our systems, and we never will.
posted by Navelgazer at 9:34 PM on September 30, 2007

1. Let's call the hole think off.
2. Christ, what an asymptote!
posted by rob511 at 9:59 PM on September 30, 2007

Navelgazer: I think you might enjoy reading about non-standard analysis.

To answer your last comment, though,

"if .99999... = 0, then there exists a problem with the system, in that two uniquely valued numbers are, in fact, not unique at all."

The answer is that these are not uniquely valued, just like 2/2 and 3/3 are not uniquely valued. They are just two different names for the same number.

If you want to invent a new system in which "1.000..." and "0.999..." are different, more power to you, but you should probably read up on what's been done before, and be prepared to present more rigorous arguments.

Incidentally, do you think that 0.3333... = 1/3?
posted by alexei at 10:38 PM on September 30, 2007

alexie, I'm nowhere near ingenuitive enough to create a new system, but that doesn't mean that the system itself isn't somehow flawed.

Also, the point I'm making, which I have trouble making because I am unfamiliar with all the terminology, isn't about any number being represented in different ways, as all numbers can be represented in an infinte amount of ways (aside from irrational numbers, of course). I referring to the, for lack of a better term, simple way of representing them, through integers and decimals.

In this way .99999... is uniquely valued as separate from 1, as are all other "simple" representations of numbers. If they truly are somehow the same, and the infinitesimal only "exists" in the same way as dragons "exist" as a concept, then there's still a systemic problem in two uniquely valued numbers equaling each other.
posted by Navelgazer at 10:53 PM on September 30, 2007

oh, you blogospherites, you crack me up. seriously, you may think all problems can be solved by yapping on and on about it and linking to more yapping elsewhere on the webternet, but sometimes you have to do things the old fashioned way by looking in a BOOK. which is exactly what i did because i'm smart. I checked my college math book (i traded a college student some weed for it) and it turns out you're all wrong.
in real life .999999.... is actually equal to four and a half.
posted by sexyrobot at 11:04 PM on September 30, 2007 [1 favorite has favorites]

and here on page 243, another proof...the "k-g theorem"
apparently not only does .9999...=4.5 but also
thing=think.
math is so cool.
posted by sexyrobot at 11:12 PM on September 30, 2007

0.999... == 1

Are you seriously proposing that 9 * (1/9) ≠ 1?

Repeating numbers are only an artifact of our writing system, and aren't even particular to decimal!

For instance: in fixed-point binary representation, the decimal number 1/10 ends up represented as 110011001100..., repeating until you run out of space in your datatype.
posted by blasdelf at 11:57 PM on September 30, 2007

nope. still 4 and 1/2. but i did get my terminology wrong...its not 'blogospherites'...its 'blogospheroids'...because of the shape of mouse potatoes.
posted by sexyrobot at 12:06 AM on October 1, 2007

if .99999... = 0, then there exists a problem with the system, in that two uniquely valued numbers are, in fact, not unique at all. This is a systemic problem.

Not so. The fact that the same number can be written in two different ways under allowable conventions of decimal representation doesn't mean that there is a problem with the system, only that it isn't a one to one mapping from decimal representations to numbers. What's happening here is that it is possible to use two unique decimal representations to refer to a single value.

Your systematic error does not exist because they are not "two uniquely valued numbers equaling each other". This simply isn't the case. Representation is not value. Sorry. 'Sin(0)' and '2-1' also share the same value as '1'.

As for infinitesimals and the extending how we deal with numbers, here's the deal: the number system used here, and in nearly all mathematical discourse ever, is called the Real number system. The reals are an extension of the rational numbers, which are in turn an extension of the integers, which are an extension of the natural numbers. When building an extension to a defined set of numbers, the new set must inherit all axiomatic properties of the earlier sets. The rational number '1' has all the same properties of the real number '1'.

It's possible to construct extenstions to the reals which include infinities and infinitesimals in meaningful ways, and it's been done. They don't get used a lot, because they're not terribly useful, but it's out there. The key is, that the real number '1' and the real number '.9r' are always the same. This is a function of the way in which the real numbers are constructed. It doesn't matter whether infinitesimals are added on or not, it doesn't change what '1' and '.9r' are, as real numbers.

What this means is, conversely, there exist number systems where '1' and '.9r' are not equal, but they must also not be real numbers. You need to change something deeper about the way in which the numbers are built than just introducing infinitesimals. Things become deeply weird when you do this. Numbers stop acting like you expect them to. They stop being useful in describing the physical world, and the world of intuitions.

So you can do it, yeah. It's been done. But it's both harder and weirder than you're thinking it should be.
posted by Arturus at 12:08 AM on October 1, 2007 [1 favorite has favorites]

I'd be willing to bet on a very strong correlation between having trouble accepting that 1=0.999... and thinking that it's "another thing" rather than "another think".

I'm pretty sure homo sapiens is actually two separate species with an intertwining reproductive strategy.
posted by lastobelus at 1:39 AM on October 1, 2007

I have to, say, I'm thorougly enjoying all the counter-arguments of this type:

By proof, they are equal to each other but otherwise they are not the same number.

The, "well, yes, using proof they are the same, or, using math they are the same, but using common sense they aren't! haha! I win!" ones.

intuition does not trump logic, people.
posted by Jon Mitchell at 1:53 AM on October 1, 2007 [1 favorite has favorites]

YOU'RE BOTH RIGHT. Now eat your beans.

Irregardless, it's the same difference.



[/ducks & throws up a little]
posted by Extopalopaketle at 2:03 AM on October 1, 2007

I've had another intensive think about it, and if I recall correctly, the number represented by .xxx... in base a is defined as the limit, as integer n approaches infinity, of x * a^-1 + x * a^-2 + x * a^-3 + ... + x * a^-n.

Because it's a limit, it's not equal to x * a^-1 + x * a^-2 + x * a^-3 + ... + x * a^-n for any integer n.

For any given integer n, there is a difference between .xxx... (which is a limit) and x * a^-1 + x * a^-2 + x * a^-3 + ... + x * a^-n (which isn't). This difference, which is equal to (a - x) * a^-(n+1), will be arbitrarily small if n is arbitrarily large, and is probably what you're thinking of when you're talking about infinitesimals.

Whenever x = a - 1, the limit is 1. So, in decimal (base 10), .999... = 1; in binary (base 2), .111... = 1.

While it's true that there's no way for a computer variable with a finite number of bits to hold a value whose representation requires an infinite number, computers can certainly represent and work with infinite series.

Anybody who enjoys this kind of argument is politely invited to watch me get schooled by Wikipedia.
posted by flabdablet at 3:25 AM on October 1, 2007

Regarding another think coming...

"that's just ugly in the mouth"

...pretty-much sums it up for me. And that sum minus one over infinity is not one, I can tell you that.
posted by Civil_Disobedient at 5:11 AM on October 1, 2007

Which is to say, if you were to ask someone to give an example of the expression "another thing coming...", it would undoubtedly start something like this: "If you think you're going out dressed like that..." or "If you think I'm washing your car with my tongue...". In each case, the phrase starts with "If you think".

If you can think of another example, you've got another think comin'...
posted by Civil_Disobedient at 5:14 AM on October 1, 2007

But I see after wandering that this point has not been lost on you fellow MeFites. Wonderful, wonderful.
posted by Civil_Disobedient at 5:27 AM on October 1, 2007

I find it absolutely fascinating that people argue -- endlessly -- about such matters. Thanks to a book I wrote about the number zero, I get all sorts of "proofs" that purport to debunk mathematical "dogma" such as 0.9999.... = 1, zero is a number, Fermat's Last Theorem is false, and so forth.

What people forget is that mathematics is not a subject that brooks debate in the usual sense. Something that is proven is objectively true: given a (consistent) set of axioms and definitions, there can be no argument contrary to something that's been proven. It simply is.

If you accept the usual axioms of mathematics, and if you accept that 0.999... is shorthand for
(lim n -> infinity) of (sum [i = 1 to n] of 9x10^(-i)])
then there's no debate; 0.999.... = 1. End of story. You have to get used to the fact that some numbers have more than one decimal representation.

You can play with the axioms somewhat; you can diddle around with non-standard analysis or surreal numbers or some other system and try to make the outcome more to your liking. You might be able to define 0.9999... in a different way and change the outcome, too. However, this misses the point -- and the beauty -- of mathematics.

Mathematics is a formal system of knowledge that allows us to discover things that are true and are vastly, vastly contrary to our intuition -- things that we would never have discovered by following our sense of aesthetics and declaring that things must simply be a certain way because they make sense. The most beautiful results in mathematics are just those that upset our intuition the most. The idea that e, i, pi, zero, one, and negative one can be related in a simple equation seems absurd. Godel's incompleteness theorem? Cantor's discovery of different levels of infinity? The Banach-Tarski paradox? I doubt that anyone would discover such things by following their aesthetic sense... these are counterintuitive and, in some ways, unaesthetic ideas.

The best mathematics will change your aesthetic and your intuition -- if you let it. That's what beautiful mathematics (and physics!) is meant to do: it is giving you a new sense of reality beyond what you already are aware of. If you reject a proven mathematical result just because it conflicts with your view of the way the world works, you're closing yourself off to a deeper understanding of the universe -- you're trying to shoehorn the universe into a tiny little box of your own creation.
posted by cgs06 at 5:29 AM on October 1, 2007 [2 favorites has favorites]

0.333... repeating for infinity.

infinity is not a real number. so this "0.333... repeating to infinity" is not a real number. Or better stated, it's not representative of a real number, whereas 1/3 is.

It's a flaw in the system we use to represent numbers. 0.333... is the closest we can come to represent 1/3 as a decimal value.

Likewise all this 1 = 0.999... sillyness.

Now in practical terms you can go ahead and equate the two as you like since difference between the two is infinitesimally small (so small it doesn't matter in any practical use). But if we're to be absolutely exact here, 1 != .0999...
posted by ruthsarian at 6:19 AM on October 1, 2007

Navelgazer, you've already more or less conceded that you don't know what mathematicians mean when they say "0.999...".

How can you disagree with them about conclusions that they've drawn about something that you know you don't know what it means?

When you say "it's a fact that 1 is not equal to 0.999...", you are not saying that "it's a fact that 1 is not equal to 1 minus the infinitesimal". If you want to say that, say that, not "it's a fact that 1 is not equal to 0.999...". Because, again, that's not what you're saying means.

Rather, you're saying that "it's a fact that 1 is not equal to the limit of the sum of (9 / (10^N)) for N from 1 to infinity".

Please describe in detail why you believe that it's a fact that 1 is not equal to the limit of the sum of (9/ (10^N)) for N from 1 to infinity.

Or else just start saying "one minus the infinitesimal is not one", and get used to mathematicians shrugging instead of stating that you're flagrantly wrong.
posted by Flunkie at 6:35 AM on October 1, 2007

And my comments above apply exactly to ruthsarian's last comment, as well.

Well, except for the "Navelgazer" part.

You don't know what a mathematician means when he says 0.9 repeating. That's absolutely clear.
posted by Flunkie at 6:37 AM on October 1, 2007

See this...
posted by aftermarketradio at 7:08 AM on October 1, 2007 [1 favorite has favorites]

Put me in the "thing" camp (I never realised anyone used "think"). Reading this thread and some of the supporting links I've worked out what has happened:

- the original phrase was "think coming", an intentionally clumsy phrase intended to be funny
- people started using "thing" instead, because a) it sounds nicer and b) it still makes sense as the phrase is commonly used
- "think" starts to diminish in usage, let's be honest, it sounds stupid and was really not that funny to start with
- as a result "thing" becomes standard
- sensible people cope with the evolving nature of language
- language pedants do not

The lesson is that language is a living, evolving think, and that language pedants are the suckiest of all pedants.
posted by theothersteve at 7:46 AM on October 1, 2007

I think armchair quarterbacking probably works better than armchair mathematics.

And thanks for your patient explanation, cgs06. I just splutter and get mad when people don't understand what math is.
posted by Nelson at 9:05 AM on October 1, 2007

Just out of curiosity, who here do you consider a "language pedant"? Because I think most of us in the "think" camp are not saying "think is right and anyone who says anything else is wrong and should get with the program." I'm certainly not, anyway, because that's completely contrary to my idea of language. The point is that think is demonstrably prior to thing, just as (say) for all intents and purposes is prior to for all intensive purposes, and you're free to say whatever you want but don't mock the people who use the prior version just because you're not familiar with it.
posted by languagehat at 9:39 AM on October 1, 2007

nitpick -- 'Sin(0)' and '2-1' also share the same value as '1'.

Cos(0) I think you mean.
posted by inigo2 at 9:42 AM on October 1, 2007

I get criticized for thinking of the apostrophe as a kind of language pendant, but that doesn’t bother me. I realize it is a doggy dog world.
posted by found missing at 10:08 AM on October 1, 2007

Doggy dog? GARGH!!

*STABBY*
posted by coriolisdave at 3:13 PM on October 1, 2007 [1 favorite has favorites]

"Thing."

I always understood the 'thing' in "You've got another thing coming" to be (undesirable) consequences.

ie: "If you think you're going out dressed like that, you've got another thing coming." meaning "If you think you're going out dressed like that, you can expect undesirable consequences from that decision/action."

Besides, Judas Priest backs me up.
posted by Extopalopaketle at 4:59 PM on October 1, 2007

I have just found out, to my considerable shock, that the otherwise well-educated ms. flabdablet thinks it's "thing".

Seems I had another think coming.
posted by flabdablet at 5:10 PM on October 1, 2007

Wow! I've also just found out that she also thinks (or thought, until I 'splained it) that .999... != 1.

Now I'm interested in the correlation. How many of those upthread who think it's "thing" also have trouble with .999... = 1?
posted by flabdablet at 5:45 PM on October 1, 2007

I have just found out, to my considerable shock, that the otherwise well-educated ms. flabdablet thinks it's "thing".


Since the phrase refers to deservedness, as in had it coming, or have it coming it seems to make more sense this way:

If you think you can waltz right in there and arrest them all by yourself, then you have it coming to you. have another thing coming to you.

It would be misleading to say that they have what they anticipate coming to them, hence, another thing. And, .9r = 1.
posted by Brian B. at 7:28 PM on October 1, 2007

Flunkie: Yes, what I'm saying is exactly that: 1 minus the infinitesimal does not equal 1. It equals 1 minus the infinitesimal. To state otherwise is biting the bullet, it seems to me. Seriously, what all of this boils down to is that there needs to be a convincing argument that the infinitesimal cannot even exist as a mathematical concept - not just in our system of what can work as usable functions, but as a mathematical concept at all - and I'll concede.

If the infinitesimal can exist as a mathematical concept, then I see no reason to trust in the man-made system of representation which can't handle it to provide proof for why it doesn't exist. It's ridiculously circular. I hold to my earlier point - it's like asking theologians to prove the existence of God, and having them quote scripture back to you as proof.

Granted, the decimal system of mathematics of almost infinitely (if you can accept the concept of ∞-1) more reliable in a logical argument than religious doctrine, you're still using the system itself to prove that the system is correct. That doesn't work logically. The system is wrong here, in either one of two ways which I've outlined above.

And people who used fractions or formulas as descriptions of how numbers can be represented in numerous ways clearly weren't getting my point, which I'll take responsibility for not illustrating clearly. When represented as integers or integers with decimals, numbers are given unique values from every other number expressed as an integer or integer with decimals.

I fail to be convinced that the infinity and the infinitesimal aren't workable and useful mathematical concepts, and eventually a new system will arise to be able to use them, particularly when the only arguments against it is that our current system of math can't make them work.
posted by Navelgazer at 7:59 PM on October 1, 2007

Following Navelgazer's logic, 1/3 != .3333....

Instead, 1/3 == .3333... + the infinitesimal.

Take that, you tunnel-visoned mathematicians stuck in your Kuhnian paradigm.
posted by found missing at 8:06 PM on October 1, 2007

- it's like asking theologians to prove the existence of God, and having them quote scripture back to you as proof.

Compare with quoting transfinite mathematics as proof of God.

Relevant commentary here.
posted by Brian B. at 8:55 PM on October 1, 2007

Navelgazer, have you truly honestly missed the point that 0.999... doesn't mean "1 minus the infinitesimal"?

Perhaps something like 0.999...9 might mean something like that; but 0.999... doesn't. The meaning of 0.999... is the limit of the sequence 0.999, 0.9999, 0.9999, ... and this limit is, by definition, 1.
posted by flabdablet at 9:45 PM on October 1, 2007

Navelgazer, here's the thing with using the system to prove the system: we are allowed to do this because the system is neither right nor wrong, the system simply is. It is the system mathematicians and everyone else finds most useful in describing our world. Other systems exist, and are useful for other things. This is not in question, and these alternative systems are equally neither right nor wrong. They simply are.

The problem you are facing is this: you are looking for a system which is objectively 'right'. No such system exists. No such judgement is possible. We only have systems which are consistent or not. 0.9r = 1 is consistent, therefore it is true. No further judgement is needed, or possible.

If the whole 'uniquely valued decimal representation' thing is throwing you off still, I offer the following solution: consider .9r to not really be a number, and then you'll be fine. "When represented as integers or integers with decimals, numbers are given unique values from every other number expressed as an integer or integer with decimals." is simply not true, but the cases where it isn't are unnecessary enough that you can fudge it like this and be fine.
posted by Arturus at 12:46 AM on October 2, 2007 [1 favorite has favorites]

inigo2: right you are.
posted by Arturus at 12:51 AM on October 2, 2007

Some contributions to this thread are painful to read. Navelgazer, ruthsarian, rainy and others, your opinion is refuted by multiple airtight deductive arguments, which you can't answer, and by the opinion of every expert (understanding the proofs that .999rec = 1 and their significance would be a precondition for being a competent mathematician), and the arguments are set out with admirable clarity in the linked posts and in some of the contributions to this thread. To respond to this by mocking the people who disagree with you, by stubbornly reiterating your opinion again and again or by invoking made-up principles like that they are "two uniquely valued numbers" is to humiliate yourself in a public forum.

Yes, there are mathematical systems that include infinitesimal quantities. That doesn't undermine the soundness of the arguments that .999rec equals 1. It's the hallmark of the crackpot to find that your opinion differs from that of every expert and conclude that every expert must therefore be wrong (or to suggest that the mathematics we all learn at school is wrong), all the while admitting that you're "not a math-wizard".

As the the other question, I always learnt it as "If you think that, you've got another think coming," and I'm surprised to learn that there are people to whom "thing" makes more sense. Language evolves, though, and if enough people mishear a word or phrase the mishearing can become standard. Maybe in the future oak trees will grow from eggcorns. It's not like mathematics where we can have deductive proofs that establish a definite truth. I agree that "thing" can make sense, maybe even more sense in some contexts. Dismissing the original, non-misheard version as "retarded" (as a couple of commenters have done) isn't exactly a mature contribution.
posted by infobomb at 5:20 AM on October 2, 2007

God, there are some pre-Madonnas in this thread...
posted by patricio at 8:42 AM on October 2, 2007

Here's a variation on the previous arguments that might have more psychological traction. Consider the quantity .111recurring . (Most of us call this one ninth, since it's what you get when you divide one by nine, but the deniers will insist it's not.) Give the deniers the benefit of the doubt and just call this x. How do you multiply x by 9? Clearly one way is to multiply each digit, giving us .999recurring.

A no less valid way is to multiply by ten, giving 1.111recurring, then subtract x once, i.e. subtract .111recurring. This gives 1.000recurring.

Since 10-1=9 (if you question that, you've got problems), these two quantities must be the same: not approximately the same, but identical. To repeat, the two quantities are 1.00000recurring and .99999recurring.
posted by infobomb at 9:46 AM on October 2, 2007

The meaning of 0.999... is the limit of the sequence 0.999, 0.9999, 0.9999, ... and this limit is, by definition, 1.

Actually, no, 0.999... is not 1 by definition. It's 1 by proof. And that proof is fundamental to how limits work and, therefore, how real analysis works. Real analysis is the fundamental of most useful mathematics, including pretty much all physics and therefore, chemistry and biology and any other mathematical science.

That's why it's so irritating when some ignorant romanticist goes on about infinitessimals and how he "feels" 0.999... isn't 1. Because the equivalence of those two numbers is rooted to a very core, productive, important part of mathematics.

I get that it's a bit counterintuitive about how 0.999... = 1, and I get that most people don't have the mathematical background to understand how this equivalence follows from basic analysis, and before it basic arithmetic and goes all the way back to the fundamental axioms of logic. Yeah, math is hard.

What I don't get is why people ignorant of mathematics don't shut the hell up.
posted by Nelson at 11:25 AM on October 2, 2007

Yeah, well, that's... like... just your opinion, man.
posted by Civil_Disobedient at 12:27 PM on October 2, 2007

ie: "If you think you're going out dressed like that, you've got another thing coming." meaning "If you think you're going out dressed like that, you can expect undesirable consequences from that decision/action."

The thing I find fascinating in this discussion is that it shows how unimportant the literal meaning of idiomatic expressions is. People say things all the time without stopping to think at all about what they literally mean ("head over heels" anyone?), but when they're forced to justify their usage they'll tie themselves in some really odd knots to retroactively defend the "logic" of their expressions. Try challenging someone on "could care less" for example.

In this "another thing coming" case several people have offered versions of the rationalization above but it's patently absurd. The problem is that it can't account for the word "another." If "you've got another thing coming" can mean "you can expect undesirable consequences from that decision" then it should be able to mean it without the preceding "if you think..." part of the phrase. In other words, it should be possible for the gangster heavies instanced earlier to come around to the guy they want to intimidate and say to him--straight off the bat--"The Bossman told us to tell you that you've got another thing coming!"--but that wouldn't sound intimidating, would it? It would sound, at best, like a promise ("I've given you things in the past, and I'll be giving you another one of them soon"). In the case above, the daughter being told "if you think you're going out dressed like that, you've got another thing coming" could only logically understand the expression to mean "I have some additional item to give you" (perhaps some additional clothes? A corsage? The address of the local strip club?). There is no logical implication that the "thing coming" will necessarily countermand her desire to go out "dressed like that."

The "another" in "another think coming" refers to the original "think" (If you think A you have another think--think B--on the way, because think A is misguided). With the "thing" variant that "another" only works in a restricted subset of uses of the expression: those in which there is some "thing" which you might be thinking that you're going to get ("if you think you're going to get thing A you have another thing coming--thing B"). But people who use the "thing" variant are happy to use it in circumstances where there is no implied "thing A" and simply don't notice that the expression is rendered meaningless in that context.

Ain't language weird? Enough to knock you head over heels.
posted by yoink at 12:49 PM on October 2, 2007

While I'm speaking solely to myself, let me tighten the above argument up a little. A "thing" advocate might say "well the 'thing A'" that the daughter expects in the above example is being able to go out dressed like that, and the 'other thing--(thing B)' that is coming to her is that she will not in fact be able to go out like that.

This is, perhaps, justifiable (although I doubt anyone has actually consciously thought something like "if the thing you think is is going to happen is that you are going to go out dressed like that" when they say "if you think..."). But that objection really can't apply to usages when it really has only to do with states of belief: e.g. "if you think .999... /= 1 then you've got another thing coming." In this case, what could possibly be the "thing A" that you originally think is "coming" and which is usurped by the unwelcome arrival of "thing B"?

On the other hand, "think" works perfectly in this case; if you think this, you'll find (on studying sufficient mathematics and logic to understand the case) that this is not a "think" that is sustainable and that you will have to adopt a different "think" in the future.
posted by yoink at 1:43 PM on October 2, 2007

Metafilter: if you think this, you'll find (on studying sufficient mathematics and logic to understand the case) that this is not a "think" that is sustainable and that you will have to adopt a different "think" in the future
posted by found missing at 1:50 PM on October 2, 2007 [2 favorites has favorites]