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Finite set
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{{Short description|Mathematical set containing a finite number of elements}} {{CS1 config|mode=cs2}} In [[mathematics]], particularly [[set theory]], a '''finite set''' is a [[Set (mathematics)|set]] that has a [[wikt:finite|finite]] number of [[Element (mathematics)|element]]s. Informally, a finite set is a set which one could in principle count and finish counting. For example, {{bi|left=1.6|<math>\displaystyle \{2,4,6,8,10\}</math>}} is a finite set with five elements. The number of elements of a finite set is a [[natural number]] (possibly zero) and is called the ''[[cardinality]] (or the [[cardinal number]])'' of the set. A set that is not a finite set is called an ''[[infinite set]]''. For example, the set of all positive integers is infinite: {{bi|left=1.6|<math>\displaystyle \{1,2,3,\ldots\}</math>}} 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|injective]] [[function (mathematics)|function]] from a larger finite set to a smaller finite set.
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