Many-to-One Relation/Examples/Square

Example of Many-to-One Relation

Let $\RR \subseteq \R \times \R$ be the relation on $\R$ defined as:

$\forall \tuple {x, y} \in \R \times \R: \tuple {x, y} \in \RR \iff x^2 = y$

Then $\RR$ is a many-to-one relation

Proof

Let:

$y_1, y_2 \in \R: \tuple {x, y_1} \in \RR \land \tuple {x, y_2} \in \RR$

Then:

$y_1 = x^2 = y_2$

and so:

$y_1 = y_2$

Hence the result.

$\blacksquare$

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): many-one correspondence