Definition:Injection/Graphical Depiction

Diagrammatic Presentation of Injection on Finite Set
The following diagram depicts an injection $f$ from $S$ into $T$:


 * $f: S \to T$

where $S$ and $T$ are the finite sets:

and $f$ is defined as:


 * $f = \set {\tuple {a, p}, \tuple {b, s}, \tuple {c, r} }$

Thus the images of each of the elements of $S$ under $f$ are:


 * Injection.png


 * $S$ is the domain of $f$.
 * $T$ is the codomain of $f$.
 * $\set {p, r, s}$ is the image of $f$.

The preimages of each of the elements of $T$ under $f$ are:

Note that $f$ is injective but not surjective:


 * $\map {f^{-1} } x$ is a singleton for all $x \in \Img f$

but:


 * $\map {f^{-1} } q = \O$