Symbols:Set Theory/Mapping

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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 .