Re: Skolem's Paradox and why is math the way it is?

From: Jonathan Hoyle (jonhoyle_at_mac.com)
Date: 09/21/04 

Date: 21 Sep 2004 06:06:32 -0700

> Why do we care about "uncountably many" real numbers when in reality
> there are only a countable number that we can "prove theorems about"?

Actually, that's not true. Although there can be only a countable
number of theorems, they can still address an uncountable number of
reals. As a simple example, there are an uncountable number of reals
in the Cantor set, and a simple procedure by which to determine given
any real if it is a member (namely, can its decimal expansion, when
convereted to base 3, be written without using the digit 1).

Jonathan Hoyle

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