> [!NOTE] Definition > A [[Function]] is binary if there exists sets $X,Y,Z$ such that $f:X\times Y\to Z$ > where $X\times Y$ is the [[Cartesian Product|cartesian product]] of $X$ and $Y$. # Examples If $X=Y=Z$, then we say that $f$ is a [[Binary Operation|binary operation]]. For example, [[Vector spaces|Scalar multiplication]] of vectors is a binary function. See more in [[Algebraic Structure]].