Lee Rudolph wrote: > Virgil <vmhjr2@comcast.net> writes: > > >Besides which, one can make > >almost any set into a vector space with enough warping. > > Of course that depends on one's (necessarily [?] informal) notion of > what "almost any" might mean when applied to the universe of sets, > but among the finite sets, "one can make" such a set X "into a > vector space" if and only if X has cardinality p^n for some prime > p and non-negative integer n; and I think it's fair (if not formally > justified) to say that not "almost any set" of finite cardinality > is a set of cardinality a prime power. No doubt some of the local > aficionados of non-naive set theory can inform us accurately of which > familiar set theoretical axioms allow one to conclude that few, many, or > "almost" all infinite sets are in bijection with some vectorspace.
"Almost any set" in this context means: "any set with either infinite cardinality or a finite prime power cardinality", as those are the cardinals of vector spaces.
