= Finite set
{wiki}
A <finite set> is a <set> admitting a <bijection> with $\{0,1,\ldots,n-1\}$ for some <nonnegative integer> $n$, including the empty set at $n=0$. The number $n$ is uniquely determined and is its <cardinality>.
Every <injective> map from a <finite set> to itself is <surjective>, and conversely. This follows by counting image elements: an injection cannot omit an element without reducing the size of its image. For infinite sets the property can fail, as $n\mapsto n+1$ is an injection of the <natural numbers> into themselves that omits zero. The bijection definition gives a precise meaning to finite without reusing the word in its own definition.
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