Definition:Zero Mapping/Vector Space

Definition
Let $Y$ be a vector space.

Let $S$ be a set.

Let $\mathbf 0_Y$ be the identity element of $Y$.

Suppose $\mathbf 0 : S \to Y$ is a mapping such that:


 * $\forall x \in S: \map {\mathbf 0} x = \mathbf 0_Y$

Then $\mathbf 0$ is referred to as the zero mapping.