Mapping/Examples/root x + root y = 1

Example of Relations which is not a Mapping
Let $R_5$ be the relation defined on the Cartesian plane $\R \times \R$ as:
 * $R_5 = \set {\tuple {x, y} \in \R \times \R: \sqrt x + \sqrt y = 1}$

Then $R_5$ is not a mapping.

Proof


$R_5$ fails to be a mapping because, for example, $\sqrt x$ does not exist for $x < 0$.

Thus $R_5$ is undefined for $x <0$.

Thus $R_5$ fails to be left-total.

We have: