Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

From: tinyurl.com/uh3t (rem642b_at_Yahoo.Com)
Date: 12/21/04 

Date: Mon, 20 Dec 2004 16:48:14 -0800

I previously commented directly on the paper full of mostly nonsense.
Now I'll comment on the second author's response to questions about it:

> If you know (in contrast to Hilbert, Kleene, Cohen, Boubaki and so on) other
> basis to differentiate infinite sets by their "cardinality" (unlike Cantor's
> theorem), please let us know and the meta-mathematical community will be
> very grateful to you for ever.

I strongly believe you are mis-characterising their knowledge of math.
I believe most/all of them would disagree with your statement that the
diagonal method is the only basis to differentiate infinite sets by
their cardinality, and each/most of them would agree with me that
testing for 1-1 correspondence between sets/subsets is the key basis
for such differentiation by cardinality. The meta-mathematical
community already knows what I know, and which you don't seem to know,
so they don't need my help, but you surely do need my help, or
somebody's help anyway.

> Yes, I never say some more deep then [sic] (1) "Cantor's Theorem on the
> uncountability of continuum is unprovable, but (2) its traditional "CDM-proof"
> is invalid".

Of what you say there, (1) is nonsense, (2) is incorrect.

> My proof is a strict isomorfic deductive model (in Tarski sense) of one
> well known invention. The invention is called the paradox of "Grand Hotel".

It's not really a paradox. It's just a property of infinite sets which
is not a property of finite sets, so when a beginning math student
first starts studying infinite sets after having previously studied
only finite sets, it's a bit surprizing. But once the surprize is over,
it makes perfect sense. For example, a countably-infinite set is like a
listing (enumeration) that just goes on and on and on, never is
finished. The thing to realize is that if you put one item in front of
it, it is retarded by one step compared to before, but still it goes on
and on and on, never is finished, just like before, so in all senses
the set with one additional element works just like the original set
without that original element. This is unlike a finite set, where the
original enumeration reaches the end at some point, but if an extra
element were inserted before it, then it hasn't yet reached the end at
that same point, it must go one more step before reaching the end. Once
you get used to the idea, maybe some of this math will make sense to
you.

You quote somebody I never heard of:
> "It is awful to think what kind of pressure the Bourbakists put on
> (evidently nonsilly) students to reduce them to formal machines! This kind
> of formalized education is completely useless for any practical problem and
> even dangerous, leading to Chernobyl-type events. ..."

That person quoted sounds as stupid as you do. I don't suppose you
considered the fact he may be stupid and talking nonsense before you
quoted him?? If you don't believe his remark is stupid, please provide
some evidence to support it. How does the study of formal mathematics
increase the likelihood of Chernobyl-type events?

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