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Topic: Cantor's first proof in DETAILS
Replies: 34   Last Post: Dec 1, 2012 10:56 AM

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
Re: Cantor's first proof in DETAILS
Posted: Nov 13, 2012 12:05 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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
>
> QED


Same 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




Date Subject Author
11/12/12
Read Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/12/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/12/12
Read Re: Cantor's first proof in DETAILS
Charlie-Boo
11/12/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Charlie-Boo
11/15/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
12/1/12
Read Re: Cantor's first proof in DETAILS
Frederick Williams
11/12/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/12/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/12/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/12/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz
11/12/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/13/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz
11/13/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/13/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/14/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/16/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/16/12
Read Re: Cantor's first proof in DETAILS
Uirgil
11/16/12
Read Re: Cantor's first proof in DETAILS
Zaljohar@gmail.com
11/16/12
Read Re: Cantor's first proof in DETAILS
LudovicoVan
11/13/12
Read Re: Cantor's first proof in DETAILS
Shmuel (Seymour J.) Metz

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