Re: Cardinality question

"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.

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


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