An interval：is a commonly used set of real numbers in mathematics . We have already learned the concept of interval in high school . For the convenience of application, we will summarize it as follows.

　　Intervals are divided into two categories finite intervals and infinite intervals.

　　1. Limited interval

　　Assume  is two real numbers, and , the number set is called an open interval, denoted as , that is

.

Similarly, closed intervals can be defined :

;

And the half-open and half-closed interval :

; .

        The real numbers  and  here are both called the endpoints of the corresponding interval ,  is the left endpoint ,  is the right endpoint , and  is the length of the interval .

　　2. Infinite interval

　　Introducing the symbols and , which are read as positive infinity and negative infinity respectively , can similarly represent infinite intervals. For example

, .

In particular, the set of all real numbers can also be expressed as an infinite interval, that is

.

　　Note: In this tutorial, when it is not necessary to specifically identify whether the interval contains endpoints, whether it is finite or infinite, it is often referred to as " interval" and is often represented by .

　　3. Graphical representation of intervals on the number axis

[ Animation ]