From: Nick Hay (nickjhay@gmail.com)
Date: Sat Aug 25 2007 - 01:46:18 MDT
On 8/24/07, Norman Noman <overturnedchair@gmail.com> wrote:
> On 8/24/07, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
>
> > You only need the axiom of choice for uncountable sets.
> >
>
> Isn't the set of all possible boxes uncountable? I assumed it was, since you
> could write write every real number on a slip of paper and put each paper in
> a box. I guess if we're limited to finite boxes that doesn't work.
You can only define notation systems which access a countable set of
numbers, never all of them. In practice, since you cannot write
10^1000 characters, there are a finite number of numbers you can
access.
-- Nick
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