> I don't know of a way to prove equipotence except by creating a 1-1 relationship between the sets in question. That relies on first defining it as "there is

> I don't know of a way to prove equipotence except by creating a 1-1 relationship between the sets in question. That relies on first defining it as "there is 1-to-1 mapping". But for sequences of numbers you could instead compare growth rates. Then the natural numbers and the even natural numbers wouldn't be the same size. Which is nice, because the latter sequence is a proper subset of the former. The former grow twice as fast, so you could say they are twice as large. But it only works for ordered sequences. Anyway, it all depends on definitions.