Date: Jan 3, 2013 5:24 PM
Author: Virgil
Subject: Re: Uncountable Diagonal Problem

In article 
<9335ba48-224c-453a-81d5-383ca8cd22cb@px4g2000pbc.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> Then, there are uncountably many nested intervals bounded by
> irrationals, and there aren't.


There are all sorts of SETS of uncountably many nested intervals bounded
by irrationals, but no SEQUENCES of them that are uncountable.

If x is any positive irrational, then [-x,x] is an interval bounded by
irrationals.

And { [-x,x] : x is a positive irrational} is a set of uncountably many
nested intervals bounded by irrationals.

But is not a sequence at all.

Get your head straight, Ross!
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