Ternary operation

Remarks

Example: on $\R$, the map $m(x, y, z)$ that returns the middle value of $x, y, z$ is a ternary operation. It is defined for every triple and its value is one of $x, y, z$, so it lies in $\R$. It satisfies $m(x, x, y) = m(x, y, x) = m(y, x, x) = x$.

Non-example: the map $(x, y, z) \mapsto x / (y - z)$ is not a ternary operation on $\R$, because it is not defined when $y = z$.

A ternary operation is usually written in prefix form $f(x, y, z)$, since there is no standard infix notation for three arguments.