Is there a word for the classification of a set as infinite or finite?
For example, in computer science, there can be zero, one, two, etc. parameters to a computer program, and this is called its "arity". Sets can be countable or uncountable. Is there some word I can use to say "this set's **___ __**" is infinite/finite, or "this set has an infinite **___ _**". For example, although this sounds terrible, "this set's finitude is infinite" or "this set has an infinite finitude".
The word population seems a natural choice, as in "This set's population is finite/infinite."