finite set

In mathematics, a set is called finite if there is a bijection between the set and some set of the form {1, 2, ..., n} where n is a natural number. (The value n = 0 is allowed; that is, the empty set is finite.) An infinite set is a set which is not finite.Equivalently, a set is finite if its cardinality, i.e., the number of its elements, is a natural number. More specifically, a set whose cardinality is n is also called an n-set. For instance, the set of integers between −15 and 3 (excluding the end points) has 17 elements, so it is finite; in fact, it is a 17-set. In contrast, the set of all prime numbers has cardinality ℵ₀, so it is infinite.
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