Definition:Left Operation

Definition
Let $S$ be a set.

For any $x, y \in S$, the left operation on $S$ is the binary operation defined as:
 * $\forall x, y \in S: x \gets y = x$

Also see
It is clear that the left operation is the same thing as the first projection on $S \times S$:
 * $\forall \tuple {x, y} \in S \times S: \map {\pr_1} {x, y} = x$

Also see

 * Definition:Right Operation