Finite Set

In mathematics, a finite set is a set that has a finite number of elements. For example,

is a finite set with five elements. The number of elements of a finite set is a natural number (non-negative integer), and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite:

Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.

Read more about Finite Set:  Definition and Terminology, Basic Properties, Necessary and Sufficient Conditions For Finiteness, Foundational Issues, Set-theoretic Definitions of Finiteness

Famous quotes containing the words finite and/or set:

    Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.
    Elizabeth Fishel (20th century)

    Reason is natural revelation, whereby the eternal father of light, and fountain of all knowledge, communicates to mankind that portion of truth which he has laid within the reach of their natural facilities: Revelation is natural reason enlarged by a new set of discoveries communicated by God immediately, which reason vouches the truth of, by the testimony and proofs it gives, that they come from God.
    John Locke (1632–1704)