Injection/Examples/Arbitrary Example 1
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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