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Topic: [HM] A question as to Cantor's Diagonal Method.
Replies: 13   Last Post: Oct 25, 2005 6:01 AM

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 MANN@vms.huji.ac.il Posts: 401 Registered: 12/3/04
Re: [HM] A question as to Cantor's Diagonal Method.
Posted: Sep 11, 2005 7:29 AM

On Sun, 4 Sep 2005, Yaakov Kupitz wrote:

.....
> for a while
> I felt that Russel's antinomy (on the set of elements which do not belong to
> themselves, see, e.g., Ebbinghaus & al, Numbers, Springer-Verlag 1991, p. 363)
> is somehow related to Cantor's Diagonal
> Process (CDP)

..........

This and earlier messages reminded me of an incident during my freshman
year here at the Hebrew University. I took a set theory course from
A.Fraenkel. That course was more or less in the spirit of F's book
Abstract Set Theory, i.e. the need for axiomatization was explained, via
Russell's antinomy, and some axioms were formulated, but not the full ZF
axiomatization, e.g. Fraenkel's own Axiom of Replacement was never mentioned.
When Fraenkel proved that a power set has a larger cardinality than the
original set (an argument that is a generalization of CDP), one of the
students remarked that actually there is nothing new in that argument,
because we've already seen the argument of Russell's antinomy. That
remark was completely mysterious to the rest of the class, and was
followed by a more or less private discussion between Fraenkel and the
student. That student, a man of great talent and promise, obtained a
Ph.D. in mathematics, but chose not to become a research mathematician.
He passed away a few months ago.

From peaceful and blue skied Jerusalem

Avinoam Mann