Mapping/Examples/x y = 1

Example of Relations which is not a Mapping
Let $R_2$ be the relation on the Cartesian plane $\R \times \R$ as:
 * $R_2 = \set {\tuple {x, y} \in \R \times \R: x y = 1}$

Then $R_2$ is not a mapping.

Proof


$R_2$ fails to be a mapping for the following reason:

For $x = 0$, there exists no $y \in \R$ such that $x y = 1$.

Thus $R_2$ fails to be left-total.