A [[Binary Operation]] $\circ$ is a [[Function]] with [[Arity]] 2 whose two [[Domain|domains]] and [[Codomain|codomains]] are the same. In other words, a [[Binary Operation]] for some [[Set]] $S$ is a [[Function|mapping]] between the [[Cartesian Product]] of $S$ with itself. $ \huge \circ :S \times S \to S $ Typically binary operations are denoted using infix notation, $x\circ y=z$. ![[../../00 Asset Bank/Pasted image 20250418014339.png|invert_S]]