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Topic: Cantor's first proof,
Replies: 115   Last Post: Nov 15, 2012 4:43 PM

 Messages: [ Previous | Next ]
 Michael Klemm Posts: 133 Registered: 11/13/12
Re: Cantor's first proof,
Posted: Nov 13, 2012 2:45 PM

WM wrote:

> Consider the set of all positive rational numbers as existing.
> Fill into the vase all numbers of the interval (0, 1]. Then enumerate
> one of them by 1 and take it off the vase.
> Fill into the vase all numbers of the interval (1, 2]. Then enumerate
> one of them by 2 and take it off the vase.
> Fill into the vase all numbers of the interval (2, 3]. Then enumerate
> one of them by 3 and take it off the vase.
> Continue until all rational numbers have been enumerated. Then all
> have been taken off the vase. The remaining set of not enumerated
> rationals is empty.

> This result is nonsense from the mathematical standpoint.

You are right, your result is nonsense. If the rational number
taken off the interval (n-1, n] is n then you define just the
identity map on N and not a map Q,>0 -> N.

Greetings
Michael

Date Subject Author
11/9/12 LudovicoVan
11/9/12 LudovicoVan
11/9/12 LudovicoVan
11/9/12 mueckenh@rz.fh-augsburg.de
11/9/12 LudovicoVan
11/9/12 mueckenh@rz.fh-augsburg.de
11/9/12 LudovicoVan
11/9/12 mueckenh@rz.fh-augsburg.de
11/9/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 Uirgil
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 Shmuel (Seymour J.) Metz
11/10/12 LudovicoVan
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 William Hughes
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/13/12 LudovicoVan
11/10/12 William Hughes
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 LudovicoVan
11/10/12 LudovicoVan
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 LudovicoVan
11/10/12 William Hughes
11/10/12 mueckenh@rz.fh-augsburg.de
11/10/12 Frederick Williams
11/10/12 Uirgil
11/11/12 William Hughes
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 William Hughes
11/12/12 William Hughes
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 William Hughes
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/13/12 LudovicoVan
11/12/12 William Hughes
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/12/12 Frederick Williams
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/12/12 Uirgil
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 LudovicoVan
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 LudovicoVan
11/12/12 mueckenh@rz.fh-augsburg.de
11/13/12 LudovicoVan
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 LudovicoVan
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/13/12 LudovicoVan
11/14/12 mueckenh@rz.fh-augsburg.de
11/14/12 Uirgil
11/14/12 Michael Klemm
11/13/12 Michael Klemm
11/13/12 Uirgil
11/13/12 mueckenh@rz.fh-augsburg.de
11/13/12 Uirgil
11/14/12 mueckenh@rz.fh-augsburg.de
11/14/12 Uirgil
11/14/12 Michael Stemper
11/14/12 Michael Stemper
11/14/12 quasi
11/14/12 quasi
11/14/12 Michael Stemper
11/14/12 mueckenh@rz.fh-augsburg.de
11/14/12 Uirgil
11/15/12 mueckenh@rz.fh-augsburg.de
11/15/12 Uirgil
11/13/12 Uirgil
11/12/12 Uirgil
11/12/12 Uirgil
11/12/12 Uirgil
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 Uirgil
11/12/12 mueckenh@rz.fh-augsburg.de
11/12/12 Uirgil
11/12/12 mueckenh@rz.fh-augsburg.de
11/10/12 Uirgil
11/10/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/11/12 LudovicoVan
11/11/12 Uirgil
11/9/12 Uirgil
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11/10/12 LudovicoVan
11/10/12 Uirgil
11/9/12 Shmuel (Seymour J.) Metz