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 $a \in A$ and $b \in B$ such that $\map f a = b$ then we can write:

$f: a \mapsto b$

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 \(f: a \mapsto b\) is f: a \mapsto 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 .

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols