Definition:Real Function

Definition
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.

Function of n Variables
The concept can be extended to as many independent variables as required.

Also see

 * Definition:Mapping: the general definition


 * Definition:Real-Valued Function