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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 4:25 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

"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




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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