Binary Operation
A binary operation on a set \(A\) is just a function \(\ast: A \times A \rightarrow A\). For any \(a,b \in A\), we write \(\ast(a,b)=a \ast b\), or \( \ast: (a,b) \rightarrow a \ast b\).
(sidenote: When context is clear, we may abbreviate \(a \ast b\) as \(ab\). )