```Date: Nov 13, 2012 12:05 PM
Author: LudovicoVan
Subject: Re: Cantor's first proof in DETAILS

"Zuhair" <zaljohar@gmail.com> wrote in message news:86a85cce-2a84-4c9f-b860-527958274b50@o8g2000yqh.googlegroups.com...<snip>> Theorem 4. for all i. x_i =/= L>> <...>>> Let J=L>> QEDSame argument, same objection: as easily proven, the limit interval here must be degenerate, that is it is the singleton (in interval notation) [L;L]. So what you claim amounts to saying that the limit value L is not in (x_n), but that is just incorrect in that if you consider the limit value, then of course it does belong to (x_n), in the limit!  More formally L = lim_{n->oo} (a_n) = lim_{n->oo} (b_n) , then just consider an injection from N* instead of N and you can even talk meaningfully about that "last value".You should rather try and show the mistake in my objection instead of proposing the same argument again and again.  As I had put it there:<< an omega-th end-point, a_oo, would necessarily be drawn from an omega-th entry of the sequence!  Formally, we have the following property:    A m : a_m e (x_n) & b_m e (x_n)That works not only for n and m in N, but also for n and m in N*.  >>Objection to Cantor's First Proof<https://groups.google.com/d/msg/sci.math/T2V4Jh7zzD8/wDM_wsyQZ0QJ>(Note that mine is against Cantor's First Proof of which yours remains a paraphrase, not a faithful reproduction.)-LV
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