Transformation monoid
= Transformation monoid
{title2=$M\subseteq X^X$}
A <transformation monoid> is a collection of <self-maps> of a fixed <set> $X$ that contains the <identity function> and is closed under <function composition>. The <associative property> comes from <function composition>. A <monoid action> describes transformations of a <set> that obey a <monoid>'s multiplication and identity laws.