\begin{definition}[Definition:Real Function]
A '''real function''' is a mapping or function whose domain and codomain are subsets of the set of real numbers $\R$.
It is frequently understood in many areas of mathematics that the domain and codomain of any function under discussion are of the set of real numbers.
Hence the adjective '''real''' is often omitted unless it is an important point to stress.
Because the concept of a '''function''' has been around for a lot longer than that of a general '''mapping''', there is a lot more terminology that has developed up round the subject, some more vague and reliant upon intuition than others.
The transcluded pages are characteristic of the presentation of the subject which is not based on a treatment of set theory.
They are included for historical interest.
\end{definition}