Date: Jan 4, 2013 4:52 PM
Author: Virgil
Subject: Re: Uncountably Nested Intervals
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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