[JadeNB]

> Parity is a property of numbers and sets only.

Why? Seriously, though: what do you mean by parity (EDIT: I mean even-ness) of a set? Almost assuredly, something like “it can be partitioned into two disjoint subsets that can be put into bijection”; but then you've just defined even-ness of cardinals (which are sets after all), and all infinite cardinals are even (in fact, satisfy 2κ = κ; EDIT: and odd; they also satisfy 2κ + 1 = κ).

[ezalor]

You read my mind for "parity of a set". So Q.E.D.: parity is only applicable to reason about numbers (and infinity is not a number). See also surreal numbers.