Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Uncountable Diagonal Problem
Posted:
Jan 3, 2013 5:24 PM
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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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