Date: Nov 13, 2012 4:25 PM
Author: LudovicoVan
Subject: Re: Cantor's first proof in DETAILS

"Uirgil" <uirgil@uirgil.ur> wrote in message 
news:uirgil-91F13B.13165013112012@BIGNEWS.USENETMONSTER.COM...

> No values which are bounded below by a strictly increasing sequence and
> bounded above by a strictly decreasing sequence are members of either
> seequence.
>
> Thus proving that, given any sequence of values in R, there must be
> values in R not appearing in that sequence.


I'll have a look at Zuhair's follow-up as soon as I manage, but let me for
now just point out that the above argument is obviously bogus: the rationals
too are dense (have the IVP as Zuhair has called it) and, by the very same
argument, we have proved that the rationals too are not countable... see?

-LV