One problem asked me to calculate the width of a doorframe, given the frame’s height and a diagonal measurement of the door. After 30 seconds’ work with pen and paper, I submitted my answer: 93.7cm.
@tylerkaraszewski: A complex number interpretation would have -1 = exp(i*pi). So -1 * -1 = exp(i*pi) * exp(i*pi) = exp(i*pi + i*pi) = exp(i*2pi). One of the properties of exp(phi) is that exp(phi + i*2pi) = exp(phi), so exp(i*2pi) = exp(0) = 1.
Is there a good answer to that question other than "because multiplication is commutative because we say so" that doesn't involve a proof from the Peano postulates?
Except you've said this to disparage an example of precisely the sort of computation one might do while doing, say, DIY. Or you might be a carpenter and do it professionally.
-1 is a unit, so the ideal it generates is the entire ring.
I'm not clear on what you mean by "negative." What's for sure is that (-1) x (-1) = 1. Doesn't matter what the ring is, it follows directly from the axioms. Because
I'm not clear on what you mean by "negative."
delmoi, what you're doing is taking the usual integers and giving them new names.
I would say that the number you call -1 is not negative, except in the very modest sense that you've chosen to express it as a string of characters starting with a "-".
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