# Interval notation

Can anyone please give a succinct and clear description on this? I'm a little confused...

Student100
Gold Member
http://www.purplemath.com/modules/setnotn.htm

Need to know where you at with it to be able to help.

Do you understand (a, b] means a isn't included in the interval but b is?

HallsofIvy
Homework Helper
(a, b) means "all numbers strictly between a and b". It can also be written as $\{x| a< x< b\}$.

[a, b) means "all numbers strictly between a and b and the number a. It can also be written as $\{x| a\le x< b\}$.

(a, b) means "all numbers strictly between a and b and the number b. It can also be written as $\{ x| a< x\le b\}$.

[a, b] means "all numbers strictlhy between a and b and both the number a and the number b. It can also be written as $\{x| a\le x\le b\}$.

In short, all of these contain the interval between a and b. "[" and "]" mean "include this end point". "(" and ")" mean "do not include this point".

(a, b) means "all numbers strictly between a and b". It can also be written as $\{x| a< x< b\}$.

[a, b) means "all numbers strictly between a and b and the number a. It can also be written as $\{x| a\le x< b\}$.

(a, b) means "all numbers strictly between a and b and the number b. It can also be written as $\{ x| a< x\le b\}$.

[a, b] means "all numbers strictlhy between a and b and both the number a and the number b. It can also be written as $\{x| a\le x\le b\}$.

In short, all of these contain the interval between a and b. "[" and "]" mean "include this end point". "(" and ")" mean "do not include this point".

Third, HOI certainly means (a,b], just in case this is not caught.