Definition:Projection (Mapping Theory)/First Projection

Definition
Let $S$ and $T$ be sets.

Let $S \times T$ be the Cartesian product of $S$ and $T$.

The first projection on $S \times T$ is the mapping $\operatorname{pr}_1: S \times T \to S$ defined by:
 * $\forall \left({x, y}\right) \in S \times T: \operatorname{pr}_1 \left({x, y}\right) = x$

Also known as
This is sometimes referred to as the projection on the first co-ordinate.

Also see

 * The left operation for the same concept in the context of abstract algebra.