Interval notation is expressing the inequality in terms of interval containing a pair of numbers. These pair represents the starting and end point and the interval tells us whether end points are included or excluded in the number line.
If a and b are given real numbers then they can be expressed by the intervals namely
  1. Open interval : It is represented as (a, b) = {x $\epsilon$ R | a < x < b}
  2. Closed interval : It is represented as [a, b] = {x $\epsilon$ R | a $\leq$ x $\leq$ b},
  3. Half open interval : It is represented as (a,b] = {x $\epsilon$ R | a < x $\leq$ b} or [a,b) = {x $\epsilon$ R |a $\leq$ x < b}.

Interval Notation Calculator represents the interval in terms of inequality and plots its graph on number line. The ( ) braces representing open interval gives open circle and [ ] braces representing closed interval gives closed circle on the graph.
Step 1: Read the problem and observe the given interval, express the intervals in terms of inequality.

Step 2 : Plot the graph on the number line using the inequality.
  1. If in inequality < or > symbols are there then use open circle and
  2. If in inequality $\leq$ or $\geq$ are there then use closed circle.

Below are given some solved problems on Interval notation which may be helpful for you.

Solved Examples

Question 1: Plot interval (0, 3) on the number line.
Solution:
 
Step 1: The given interval is (0, 3). The inequality notation is given by 0 $\leq$ x < 3. Hence the integer solutions are
                      x = 0
                      x = 1
                      x = 2

Step 2 : Hence the graph will have close circle at 0 and open circle at 3.
Interval Notation

 

Question 2: Plot interval (-1, 6) on the number line.
Solution:
 
Step 1: The given interval is (-1, 6). The inequality notation is given by -1 < x $\leq$ 6. Hence the integer solutions are
                        x = 0
                        x = 1
                        x = 2
                        x = 3
                        x = 4
                        x = 5
                        x = 6

Step 2 : Hence the graph will have open circle at -1 and closed circle at 6.
Interval Notation