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)
“But whatever happens, wherever the scene is laid, somebody, somewhere, will quietly set out—somebody has already set out, somebody still rather far away is buying a ticket, is boarding a bus, a ship, a plane, has landed, is walking toward a million photographers, and presently he will ring at my door—a bigger, more respectable, more competent Gradus.”
—Vladimir Nabokov (1899–1977)