Definition:Bijection/Graphical Depiction

Diagrammatic Presentation of Bijection on Finite Set
The following diagram illustrates the bijection:
 * $f: S \to T$

and its inverse, where $S$ and $T$ are the finite sets:

and $f$ is defined as:


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

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


 * Bijection-and-Inverse.png


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

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

$f$ is surjective and injective:


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