On Thursday, 27 June 2013 11:52:27 UTC+2, fom wrote:
> It is one thing to speak of "strokes-as-numerals"
So did Cantor: "Da aus jedem einzelnen Elemente m, wenn man von seiner Beschaffenheit absieht, eine "Eins" wird, so ist die Kardinalzahl M selbst eine bestimmte aus lauter Einsen zusammengesetzte Menge" (The cardinal is a set constituted of ones.)
> and mimic arguments that are in the literature.
That's your main occupation.
> It is a different thing to work without axioms or logic and mangle different subjects senselessly.
If you worked with logic and axioms, you could conclude from A > 1 (which has been defined by set theory) on 1/A < 1. You could even prove it.
Of course matheologians try to escape the comparison of matheology with mathematics. But aleph_0 > 1 has been put! That cannot be denied. Withdraw it, and everybody can see that matheology is independent of mathematics and vice versa. Then you may play your meaningsless games without being disturbed by mathematicians.