
Re: Problems with Infinity?
Posted:
Apr 11, 2013 9:49 PM


On Apr 11, 6:40 pm, Walter Bushell <pr...@panix.com> wrote: > In article <512CA332.AD4F7...@btinternet.com>, > Frederick Williams <freddywilli...@btinternet.com> wrote: > > > That the cardinality of the continuum (c = 2^{aleph_0}) is equal to > > aleph_1 is Cantor's continuum hypothesis which modern set theory settles > > neither one way nor the other. > > Does anyone care. That is do any important results hang on either one?
Well, it's hard for me to imagine what form a set with an intermediate cardinality could take. So, if one were exhibited, that would be fascinating.
However, there is a set known to have cardinality aleph1, the set of wellorderings of the integers. So, if people could just get that set clearly explained, it would be clear if it could or could not be put into onetoone correspondence with the reals.
John Savard

