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Matheology § 155
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WM  
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 More options Nov 19 2012, 4:58 am
Newsgroups: sci.logic, sci.math
From: WM <mueck...@rz.fh-augsburg.de>
Date: Mon, 19 Nov 2012 01:58:03 -0800 (PST)
Local: Mon, Nov 19 2012 4:58 am
Subject: Matheology § 155
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Matheology § 155

At first it seems obvious, but the more you think about it, the
stranger the deductions from this axiom seem to become; in the end you
cease to understand what is meant by it. (Bertrand Russell about the
Axiom of Choice)
[Naum Yakovlevich Vilenkin: "In search of infinity", Birkhäuser,
Boston (1995) p. 123]
http://books.google.de/books?id=cU3HQFek7L0C&printsec=frontcover&sour...

The axiom of choice is obvious. But there are no uncountable sets.
Therefore the impossible task vanishes that elements must be well-
orderable without the possibility to distinguish and identify them.

Regards. WM


 
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Vurgil  
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 More options Nov 19 2012, 4:54 pm
Newsgroups: sci.logic, sci.math
From: Vurgil <Vur...@arg.erg>
Date: Mon, 19 Nov 2012 14:54:27 -0700
Local: Mon, Nov 19 2012 4:54 pm
Subject: Re: Matheology 155
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In article
<a2e4d7c5-5f22-456c-91fe-0adfc5859...@ez26g2000vbb.googlegroups.com>,

 WM <mueck...@rz.fh-augsburg.de> wrote:
> [Naum Yakovlevich Vilenkin: "In search of infinity", Birkh user,
> Boston (1995) p. 123]
> http://books.google.de/books?id=cU3HQFek7L0C&printsec=frontcover&sour...
> _summary_r&cad=0#v=onepage&q=&f=false

It is quite possible to do a great deal of mathematics without the axiom
of choice, but it is usually much more difficult, and the odd results
that that axiom sometimes alows one to produce do not seem to effect
anything essential.

 
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