> 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."