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Finite set

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


{2, 4, 6, 8, 10} 
is a finite set with five elements. The number of elements of a finite set is a natural number (a 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:


{1, 2, 3, …}.
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.

Usage examples of "finite set".

Even if he gets some of the letters and numbers wrong, were dealing with a finite set, you know, the fifty-five hundred stars or star systems within eighty light-years or so--I havent looked up the exact number.

Even if he gets some of the letters and numbers wrong, we're dealing with a finite set, you know, the fifty-five hundred stars or star systems within eighty light-years or so-I haven't looked up the exact number.

They'd make do with a finite set of traits, and pass those on to future generations the way every other life-form does.

It is construed according to a finite set of grammatical rules, constituting a program capable in principle of infinite enunciation.