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:


 * $\forall x, y \in S: x \leftarrow y = x$

It is clear that the left operation is the same thing as the first projection on $S \times S$:
 * $\forall \left({x, y}\right) \in S \times S: \operatorname{pr}_1 \left({x, y}\right) = x$

Also see

 * Definition:Right Operation