## Domain and range

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