**Functions.**
A function is a ``correspondence'' from each element of a set
to ``exactly'' one element of a set .
The *domain* of is always the set itself,
but the *range* of must be defined as the subset of consisting
of all possible values for in .
In mathematical terms the range of can be expressed as

For example, both the domain and the range of a linear function are given by the set of entire real numbers. In other words, .

**Intervals.**
An *interval* is a set of real numbers
``between two *endpoints*,'' say and .
Depending on whether it includes endpoints or not, and whether it is
finite or infinite, the following types of an interval are considered.

Finite interval | Notation |

Infinite interval | Notation |

The set of all real numbers can be viewed as a special case of interval, denoted by .

Department of Mathematics