Definition:Left Operation

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Let $S$ be a set.

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

$\forall x, y \in S: x \gets y = x$

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It is clear that the left operation is the same thing as the first projection on $S \times S$:

$\forall \tuple {x, y} \in S \times S: \map {\pr_1} {x, y} = x$

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  • Results about left operation can be found here.