Ralf Bader wrote: [...] > 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...
Indeed. Mueckenhein's powers of confusion really are wasted: he could surely have had a really successful career as a lawyer (or perhaps it doesn't work like that in Germany).
Anyway, it can all be done so much more simply:
Theorem: All infinite sets can not [orthography sic] be distinguished by sizing
Definition: A sizing is an attempt to mark off all elements of a set, one at a time. (We observe that sizing is a good way to distinguish the set of primary colours from the set of days of the week. We also note that if sizing fails on two sets, it cannot be used to distinguish them.)
Proof: Any attempt to size an infinite set fails, because the process never ends. QED