# Symbols:Set Theory/Mapping

## Mapping

A mapping $f \subset A \times B$ can be written:

$f: A \to B$

or:

$A \stackrel {f} {\longrightarrow} B$

If $f$ is an injection this can be written:

$f: A \rightarrowtail B$ or $f: A \hookrightarrow B$

Similarly a surjection can be written:

$f: A \twoheadrightarrow B$

Notations for bijection include:

$f: A \leftrightarrow B$ or $f: A \stackrel {\sim} {\longrightarrow} B$

The $\LaTeX$ code for these symbols are as follows:

The $\LaTeX$ code for $f: A \to B$ is f: A \to B .
The $\LaTeX$ code for $A \stackrel {f} {\longrightarrow} B$ is A \stackrel {f} {\longrightarrow} B .
The $\LaTeX$ code for $f: A \rightarrowtail B$ is f: A \rightarrowtail B .
The $\LaTeX$ code for $f: A \hookrightarrow B$ is f: A \hookrightarrow B .
The $\LaTeX$ code for $f: A \twoheadrightarrow B$ is f: A \twoheadrightarrow B .
The $\LaTeX$ code for $f: A \leftrightarrow B$ is f: A \leftrightarrow B .
The $\LaTeX$ code for $f: A \stackrel {\sim} {\longrightarrow} B$ is f: A \stackrel {\sim} {\longrightarrow} B .