Function terminology

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Table of terms

For a function $f:A\rightarrow B$ where $A$ and $B$ are assumed to be any set unless stated otherwise we say the following about $f$:

Term	$A$'s structure	$B$'s structure	Definition	Comment
Numerical function on $A$		$\overline{\mathbb{R} }=\mathbb{R}\cup\{-\infty,\infty\}$	$f:A\rightarrow\overline{\mathbb{R} }$
Positive valued function on $A$		$\overline{\mathbb{R}_{\ge 0} }=\mathbb{R}_{\ge 0}\cup\{+\infty\}$	$f:A\rightarrow\overline{\mathbb{R}_{\ge 0} }$
Real valued function on $A$		$\mathbb{R}$	$f:A\rightarrow\mathbb{R}$

See also

• Extended real value