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} where n is a natural number. All finite sets are countable, but not all countable sets are finite.

Related Topics:
Mathematics - Set - Bijection - Natural number - Countable

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It is a theorem (assuming the axiom of choice) 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.

Related Topics:
Theorem - Axiom of choice - Subset - Cardinality - Integer - Prime number - Infinite

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In physics, finite additionally means "non-zero", for instance in a sentence like "if the distance of the two objects is finite...".

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See also: infinity

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