In article <email@example.com>, firstname.lastname@example.org wrote:
> On Wednesday, 19 June 2013 14:12:36 UTC+2, Peter Percival wrote: > > email@example.com wrote: > > Look: Zermelo has "proved" that the > > real numbers can be well-ordered. But it has been proved that the real > > numbers in fact cannot be well-ordered. That is as certain as that you > > cannot get a 13 with two dice. I think you're confusing two different > > results. > > > But your thinking is mistaken. It is obvious that the reals have not yet been > well-ordered. If there had been a positive result, everybody would know it. >
> 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". What he may have proved is that given the axioms of ZFC, THEN "every set can be well-ordered", which is quite different.
> 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 outside Wolkenmuekenheim, since the world WM claims to live in is not at all the same world that the rest of us live in. --