Finite

In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} with n∈N. It is a theorem that a set is finite if and only if there exists no bijection between the set and any of its proper subsets. Equivalently, a set is finite if its cardinality, i.e. the number of its elements, is a natural number. For instance, the set of integers between -15 and 3 is finite, since it has 17 elements. The set of all prime numbers is not finite. Sets that are not finite are called infinite.

In physics, the term finite is in addition used in the meaning of "non-zero", for instance in a sentence like "if the distance of the two objects is finite...".

See also: infinity, countable set

pl:Zbiór skończony uk:Скінченна множина

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