Re: Proof of ordered powerset

From: Dave Rusin (rusin_at_vesuvius.math.niu.edu)
Date: 03/21/05 

Date: 21 Mar 2005 20:23:17 GMT

>its like saying that sqrt(2) is finite, but what is sqrt(2)? well, if its
>1.414213.... then its infinite, but if its sqrt(2) its not? what if we are
>in base sqrt(2)?

This is why mathematicians clump together at parties, apart from
everyone else. It must be exasperating for non-mathematicians to face
these questions without hard-and-fast definitions that make all of
this instantly resolvable, but it's just as exasperating for
mathematicians to have to back all the way up to first principles and
explain the definitions. So They mingle together over there by the canapes
and We stand here by the drinks, until it's time to talk politics
or sports. Otherwise...

A. It's the number whose square is 2.
A. Well, that's a consequence of the intermediate value theorem.
A. It follows from the Completeness axiom.
A. Well, you could use Dedekind cuts or Cauchy sequences. You accept Q, first?

[And on it would go. We haven't even gotten to "is finite".]

dave

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