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

• Right Operation

Sources

• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 2$: Example $2.4$