LudovicoVan
Posts:
4,025
From:
London
Registered:
2/8/08


Re: Cantor's first proof in DETAILS
Posted:
Nov 13, 2012 4:25 PM


"Uirgil" <uirgil@uirgil.ur> wrote in message news:uirgil91F13B.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 followup 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

