Editing Finite set (section)

== Definition and terminology ==

Formally, a set <math>S</math> is called '''finite''' if there exists a [[bijection]]
{{bi|left=1.6|<math>\displaystyle f\colon S\to n</math>}}
for some natural number <math>n</math> (natural numbers are defined as sets in [[Zermelo-Fraenkel set theory]]).  The number <math>n</math> is the set's cardinality, denoted as <math>|S|</math>.

If a nonempty set is finite, its elements may be written in a [[sequence]]:
{{bi|left=1.6|<math>\displaystyle x_1,x_2,\ldots,x_n \quad (x_i \in S, \ 1 \le i \le n).</math>}}
<br/>If ''n''≥2, then there are multiple such sequences.
In [[combinatorics]], a finite set with <math>n</math> elements is sometimes called an ''<math>n</math>-set'' and a [[subset]] with <math>k</math> elements is called a ''<math>k</math>-subset''.  For example, the set <math>\{5,6,7\}</math> is a 3-set&nbsp;– a finite set with three elements&nbsp;– and <math>\{6,7\}</math> is a 2-subset of it.