Definition:Projection (Mapping Theory)

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

First Projection
The first projection on $$S \times T$$ is the mapping $$pr_1: S \times T \to S$$ defined by:

$$\forall \left({x, y}\right) \in S \times T: pr_1 \left({x, y}\right) = x$$

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

Second Projection
The second projection on $$S \times T$$ is the mapping $$pr_2: S \times T \to T$$ defined by:

$$\forall \left({x, y}\right) \in S \times T: pr_2 \left({x, y}\right) = y$$

This is sometimes referred to as the projection on the second co-ordinate.