Re: Cardinality question

On Fri, 08 Apr 2005 02:58:44 GMT, "Larry Hammick"
<larryhammick@xxxxxxxxxxxxxxxx> wrote:

>"fishfry"
>> In article <42555143.4050504@xxxxxxxxxxxxxxxxxxx>,
>> Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:
>>
>>
>> > Can you please enlighten me whether all Cantorian cardinality stuff is
>> > useful for anything else than joking?
>I could live nicely without any uncountable ordinals or cardinals,
>and I venture to say that so could most professional mathematicians
>(which I'm not). But -- just for example -- how could we talk about
>the existence of a solution of a differential equation, without using
>transfinite induction in some form and at some level? Even the
>claim that any vector space has a basis relies on Zorn or some
>equivalent.
>>
>> Are you friends with Mike Deeth? I believe he is the one who started
>> talking about the "Cantorians" and their evil theories.
>Haven't seen him lately. Maybe he turned 12 and retired.
>
>This Cantor-was-wrong jazz has many precedents in history.
>I suspect that the Cantor issue is picking up steam again
>because _computers_ are helpless with infinite sets.

Uh, do you have any reason to think that there is such a
"movement", which is picking up steam, other than the
crackpot posts here on sci.math?

>It's true that transfinite induction leaves something to
>be desired in "intuitive" trustworthiness. But the history of
>analysis is very long and rather painful, and it's not over yet.
>
>Historical note! The topologist Kuratowski published Zorn's
>lemma long before Zorn rediscovered it.
>Kuratowski: Fund. Math. 5 (1922) pp. 76-108.
>Zorn: Bull. AMS 41 (1935) pp. 667-670.
>
>LH
>


************************

David C. Ullrich
.

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