
Re: Problems with Infinity?
Posted:
Apr 11, 2013 11:27 PM


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.)

