Virgil
Posts:
8,833
Registered:
1/6/11


Re: Problems with Infinity?
Posted:
Apr 12, 2013 12:50 AM


In article <bb3aebb3658d44439934d0cb066af67a@q9g2000yqd.googlegroups.com>, Butch Malahide <fred.galvin@gmail.com> wrote:
> On Apr 11, 8:49 pm, Quadibloc <jsav...@ecn.ab.ca> wrote: > > > > However, there is a set known to have cardinality aleph1, the set of > > wellorderings of the integers. > > Well, sort of. Actually, the set of wellorderings of the integers has > the cardinality of the continuum, which may or may not equal aleph_1. > It's the set of *order types* of wellorderings of the integers that > absolutely has cardinality aleph_1. That is, you definite an > equivalence relation on that set of wellorderings, two orderings > being called equivalent just in case they are isomorphic, and the the > resulting equivalence classes are aleph_1 in number. (That's what you > meant, but mathematicians make a big deal of saying what you mean and > meaning what you say.)
Which rules out WM. 

