On Friday, 21 June 2013 21:53:31 UTC+2, Virgil wrote:
> > The axiom of choice leads to the well-ordering theorem. Zermelo proved "every set can be well-ordered", which is literally a lie.
> It is a lie to claim that Zermelo proved "every set can be well-ordered".
Beweis, daß jede Menge wohlgeordnet werden kann. (1904)
> What he may have proved is that given the axioms of ZFC, THEN "every set can be well-ordered", which is quite different.
No. At those times people did not use nonsense-axiom and derive other nonsense from them - like matheologians today do without being ashamed. At those times axioms had to be meaningful. Compare the discussion about the "validity" or "truth" of the axiom of choice.
> > We know that it is > impossible to well-order any uncountable set because there are only countably many marks which can be attached to the elements.
> What WM claims to "know" is neither evidence nor necessarily true anywhere
It is obviously ture everywhere. Why else should matheologians try to "construct" such a blatant idiocy as uncountable alphabets?