A [[Semigroup]] in abstract algebra is a weakened notion of a [[Group|group]], and a stronger notion of a [[Magma]]. A [[Semigroup]] consists of an [[Underlying Set|underlying set]] $S$ and a [[Binary Operation|binary operation]] $\circ$ that is [[Associative Property|associative]] and [[Closure|closed]] under $S$. In othe words, a [[Semigroup]] is a [[Magma]] with an [[Associative Property|associative]] [[Operation|operator]]. Alternatively, a [[Semigroup]] is a [[Group]] without the requirement for a [[Identity Property|identity]] or [[Inverse Property|inverse]]. $\huge \begin{align} \end{align} $