A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted left bracketing bar X right bracketing bar or #X. In other words, X is equipollent to the set {1, ..., n}. We simply say that X has n elements. The empty set is also considered as a finite set, and its cardinal number is 0. A finite set can also be characterized as a set which is not infinite, i.e., as a set which is not equipollent to any of its proper subsets. In fact, if Y subset X, and Y!=X, a certain number a of elements of X do not belong to Y, so that left bracketing bar Y right bracketing bar = n - a

empty set | infinite set | set | universal set