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

• Results about left operation can be found here.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Example $2.4$