A set S is finite if there exists a natural numberMathworldPlanetmath n and a bijection from S to n. Note that we are using the set theoretic definition of natural number, under which the natural number n equals the set {0,1,2,,n-1}. If there exists such an n, then it is unique, and we call n the cardinality of S.

Equivalently, a set S is finite if and only if there is no bijection between S and any proper subsetMathworldPlanetmathPlanetmath of S.

Title finite
Canonical name Finite
Date of creation 2013-03-22 11:53:25
Last modified on 2013-03-22 11:53:25
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Definition
Classification msc 03E10
Classification msc 92C05
Classification msc 92B05
Classification msc 18-00
Classification msc 92C40
Classification msc 18-02
Related topic InfiniteMathworldPlanetmath
Defines finite setMathworldPlanetmath