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