Injection/Examples/Arbitrary Example 1

Example of Injection

Let $S$ be the set $\set {3, 6}$.

Let $T$ be the set $\set {9, 36, 150$.

Let $f: S \to T$ be the square function:

$\forall x \in S: \map f x = x^2$

Then $f$ is an injection.

Proof

We have:

\(\ds \map f 3\)

\(=\)

\(\ds 9\)

\(\ds \map f 6\)

\(=\)

\(\ds 36\)

Hence by definition $f$ is an injection.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): injection
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): injection