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<p><a href="page.php?w=semigroup">semigroup</a> for the history of the subject, and some other general properties of monoids.</p>

<p><big> Definition </big></p>
<p>A <a href="page.php?w=set_%28mathematics%29">set</a>  equipped with a <a href="page.php?w=binary_operation">binary operation</a> , which we will denote , is a <b>monoid</b> if it satisfies the following two axioms:</p>

<p>; Associativity: For all ,  and  in , the equation  holds.; Identity element: There exists an element  in  such that for every element  in , the equalities  and  hold.</p>

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