Laws of Composition
Def. (Laws of Composition) any rule combining pairs of element of S to get another element of S: #S\times S \to S#.
Def. (Associative law) Skipped
Prop. 2.1.4 (Associative law #\Leftrightarrow# Product Def.): #[a_1] = a_1, [a_1a_2] = a_1\times a_2, \forall integer i in range [1,n], [a_1\cdots a_n] = [a_1\cdots a_i][a_{i+1}\cdots a_n].
Def. (Identity) #ea=a and ae=a, \forall a \in S#