Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Uncountably Nested Intervals
Posted:
Jan 4, 2013 4:52 PM
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In article
<d59d0c5c-427f-4855-bf5e-af25b2dc47ac@t6g2000pba.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> > So Ross was wrong, and too chicken to own up.
> > --
>
> No, what I said was there are and aren't. I simply constructed
> examples where there are and examples where there could not be.
> That's a poor and ungenerous representation. Your argument is simply
> fallacious
Ross stated that there were no sets of nested intervals with irrational
endpoints which could be uncountable, and therefore not sequences.
He was wrong.
{ [-x,x] : x is a positive irrational} is just such a set of uncountably
many nested intervals. I.e., given any 2 of them one, is a subset of the
other.
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