Re: Cantor's diagonal proof wrong?
From: Todd Trimble (trimble1_at_optonline.net)
Date: 12/01/04
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Date: Wed, 1 Dec 2004 16:10:51 +0000 (UTC)
On 01 Dec 2004, Todd Trimble wrote:
>On 30 Nov 2004, The Ghost In The Machine wrote:
>>In sci.math, Shmuel (Seymour J.) Metz
>><spamtrap@library.lspace.org.invalid>
>> wrote
>>on Sun, 28 Nov 2004 00:57:39 -0500
>><41a968d3$6$fuzhry+tra$mr2ice@news.patriot.net>:
>>> In <20041125220813.662$cO@newsreader.com>, on 11/26/2004
>>> at 03:08 AM, curt@kcwc.com (Curt Welch) said:
>>>
>>>>But it is still curious that it happens at 2^oo and not oo^oo.
>>>
>>> Why? Is it curious that 3*3 is smaller than 3^3, or that 16*16 is
>>> smaller than 2^16?
>>>
>>
>>I suspect that, if a set S has cardinality of at least card(N),
>>then a bijective mapping can be found between the elements of 2^S
>>and the elements of n^S, where n > 1 is an integer.
>>
>>However, I'd have to look.
>>
>
>Sure, that's correct; in fact, n can have cardinality anywhere
>from 2 to 2^S. There's an injection 2^S --> n^S, and there's
>an injection n --> 2^S (and so an injection
>
> 2^S --> (2^S)^S ~ 2^S);
>
>now apply Schroeder-Bernstein.
>
>Todd Trimble
Typo: displayed line should read n^S --> (2^S)^S ~ 2^S.
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