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