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Re: Matheology § 127
Posted:
Oct 23, 2012 7:33 PM
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FredJeffries wrote:
> On Oct 23, 1:10 pm, Virgil <vir...@ligriv.com> wrote:
>>
>> How about the infinite set of finite complex numbers with the infinite
>> set of finite integers? Can you intercede them?
>
> Isn't this trivial? Just map the integers 1 to 1 onto the rationals
> and the
> complex numbers 1 to 1 onto the irrational numbers under the normal
> ordering.
>
> What did I miss?
I don't know what you missed, as all this is the typical Mückenheimian
muddled crap.
What is a "finite complex number"? Are there any non-finite complex numbers?
However, as you can see from
http://planetmath.org/?op=getobj&from=corrections&id=11892#
the purpose of the whole thing is to obtain a notion which is unable to
distinguish in any way between infinite sets of "numbers",
whatever "numbers" may be here. And the inventor of the dull idea
of "intercession" ridiculously believes that presenting such a notion would
throw the notion of cardinality out of business. This of course the notion
of intercession doesn't do and moreover, there is an obvious notion which
achieves the task of not being able to distinguish between infinite sets,
namely the notion of infinite set. That was the first point, the idiocy in
the beginning.
The second is, if one really wants to define that notion of intercession
then one wouldn't do this in the idiotically awkward way of Mückenheim. One
might say: Two disjoint sets A, B are in intercession if there is a linear
ordering of the union A u B such that A as well as B is a dense subset in
that ordering; with some additional ado in the case that A and B are not
necessarily disjoint. "distinction of identical elements" may be achieved
by replacing elements a e A with the ordered pair (a,0) and b e B with
(b,1) or something like that. But no ado about "sets of finite numbers".
That was the second point, setting Mückenheim's idiotic definition
straight.
And now the third point: This relation of intercession, as just defined, is
not an equivalence relation, because (PA being the power set of A) A and
PPA can never be in intercession, but infinite A and PA are in intercession
at least if the (generalized) continuum hypothesis applies. This is an
assertion of exercise level, but surely beyond Mückenheim's grasp.
Ralf
--
Neueste Forschungsergebnisse aus deutschen Spitzenhochschulen. Heute von
Prof. Dr. Wolfgang Mückenheim, Mathematikkoryphäe der FH Augsburg, aus
seiner Postille "Physical constraints of numbers": "Even some single
numbers smaller than 2^10^100 ... do not exist."
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