PLEASE CLOSE THIS WINDOW WHEN

YOU ARE FINISHED WITH IT.

### Interval

A set I of real numbers is an **interval** if it has the following special property:
Whenever a and c are in I and a < b < c, then c is in I.

There are several types of intervals. Suppose first that a and b are real numbers. Here are four different kinds of intervals of finite length.
**open interval**: (a, b) = {x in **R** : a < x < b}

**closed interval**: [a, b] = {x in **R** : a <= x <= b}

**half-open interval**: (a, b] = {x in **R **: a < x <= b}

other **half-open interval**: [a, b) = {x in **R** : a <= x < b}

There are five kinds of intervals of infinite length, sometimes called **rays**.
(a, +infinity) = {x in **R**: a < x}

[a, +infinity) = {x in **R**: a <= x}

(-infinity, a) = {x in **R**: x < a}

(-infinity, a] = {x in **R**: x <= a}

(-infinity, infinity) = **R**

Make particular note of the fact that infinity is not a real number, and neither is -infinity. The word infinity is simply used as a convenient label for a useful concept.