finite

Basically, a set is finite if you can count the number of elements in it. Above, we see a formal notion of counting in the bijection between the given set X and the set of the first n natural numbers.

Fi"nite (?), a. [L. finitus, p.p. of finire. See Finish, and cf. Fine, a.]

Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.

© Webster 1913.