Image is Subset of Codomain/Corollary 3
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Corollary to Image is Subset of Codomain
Let $f: S \to T$ be a mapping.
The image of $f$ is a subset of the codomain of $f$:
- $\Img f \subseteq T$
Proof
We have that a mapping is by definition also a relation.
The result follows from Image is Subset of Codomain: Corollary 1.
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): function (map, mapping)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): function (map, mapping)