Definition:Right Operation

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Definition

Let $S$ be a set.

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

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

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

$\forall \left({x, y}\right) \in S \times S: \operatorname{pr}_2 \left({x, y}\right) = y$