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:
“All finite things reveal infinitude:”
—Theodore Roethke (1908–1963)
“Colleges, in like manner, have their indispensable office,—to teach elements. But they can only highly serve us, when they aim not to drill, but to create; when they gather from far every ray of various genius to their hospitable halls, and, by the concentrated fires, set the hearts of their youth on flame.”
—Ralph Waldo Emerson (1803–1882)