# Great lines of numbers, all bright and shiny.

September 21, 2011 6:29 AM Subscribe

This post was deleted for the following reason: Maybe do this tomorrow without the stunty framing. -- cortex

Oddly enough, there are as many real numbers as there are half as many real numbers.

This fact let me cut my study time in math classes by 1/2.

posted by twoleftfeet at 6:40 AM on September 21, 2011

This fact let me cut my study time in math classes by 1/2.

posted by twoleftfeet at 6:40 AM on September 21, 2011

How many real numbers are there on Facebook? (I ask because I went on a date with one but she turned out to be really irrational.)

posted by Potomac Avenue at 6:42 AM on September 21, 2011 [1 favorite]

posted by Potomac Avenue at 6:42 AM on September 21, 2011 [1 favorite]

Most of the real numbers on Facebook are irrational where "most" is literally "infinitely more than".

posted by DU at 6:48 AM on September 21, 2011

posted by DU at 6:48 AM on September 21, 2011

An uncountable infinity is nothing you can count on.

posted by twoleftfeet at 6:53 AM on September 21, 2011

posted by twoleftfeet at 6:53 AM on September 21, 2011

In case you didn't RTFA,

posted by Obscure Reference at 6:54 AM on September 21, 2011

*How is the winner decided? Well, the organizer has chosen a well-ordering of the real numbers (i.e., the points on the dartboard), say <>> M, and you win.*

But the situation is entirely symmetrical, and so by the same argument, with probability 1, I win.But the situation is entirely symmetrical, and so by the same argument, with probability 1, I win.

posted by Obscure Reference at 6:54 AM on September 21, 2011

I left out the beginning:

posted by Obscure Reference at 6:55 AM on September 21, 2011

*You and I are throwing darts at a dartboard. We are separated by a screen, so that nothing either of us does can influence the other. At a given signal from a third party, we both throw a dart at the board. We do so entirely randomly. (Formally, since the points on the dartboard can be put into a one-one correspondence with the real numbers, we are simply two independent random number generators.)*posted by Obscure Reference at 6:55 AM on September 21, 2011

*Suppose the Continuum Hypothesis were true. Then the organizer could have chosen the well-ordering so that, for any number X, the set {R|R less than X} is countable.*

I don't understand how the assumption of the Continuum Hypothesis makes that well-ordering possible.

(I have replaced the symbol << with "less than" because the << seems to be messing up the html formatting here.)

posted by GentleReader at 7:06 AM on September 21, 2011

Well ordering comes from the axiom of choice. (Every set can be well ordered.)

posted by Obscure Reference at 7:11 AM on September 21, 2011

posted by Obscure Reference at 7:11 AM on September 21, 2011

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How many real numbers are there? [more inside]ISWYDT

posted by DU at 6:36 AM on September 21, 2011 [2 favorites]