Notation and Symbols
You have used many different notations and symbols in your study of
mathematics, including exponential notation and ordering symbols. Here
are some examples for you to review.
A positive integer exponent is used to indicate repeated multiplication of a
number.
For example, the expression 7^{3} is written in exponential notation. It
means 7 Â· 7
Â· 7. The exponent is 3 and the base is 7.
Ordering symbols are used to indicate the relative position of two
numbers on a number line. The number on the left is less than the number
on the right.
For example, 4 is less than 2 because 4 lies to the left of 2.
Symbol 
Meaning 
Example 
Position on Number line 
= 
is equal to 

Same position. 
≠ 
is not equal to 
4
≠ 2 
Different position. 
< 
is less than 
4 < 2 
4 is to the left of 2. 
> 
is greater than 
2 > 4 
2 is to the right of 4. 
≤ 
is less than or equal to 
4 ≤ 2
4 ≤ 4 
4 is to the left of 2. Same position. 
≥ 
is greater or equal to 
2 ≥ 4
4 ≥ 4 
 is to the right of 4. Same position. 
Note
The pointed end of the inequality symbol
always points towards the smaller number.
Thus, â€œfour is less than sevenâ€ is written
4 < 7.
Likewise, â€œseven is greater than fourâ€ is
written 7 > 4.
Example 2
Which of the following statements are true?
a. 6 > 2
b. 5 < 3
c. 7 ≤ 7
Solution
a. False. 6 > 2 is read â€œnegative six is greater than negative two.â€
This statement is false because 6 lies to the left of
2 on the number
line. Therefore, 6 < 2.
b. True. 5 < 3 is read â€œnegative five is less than three.â€
This is true because 5 lies to the left of 3 on the number line.
c. True. 7 ≤
7 is read â€œseven is less than or equal to 7.â€
This means either â€œ7 is less than 7â€ or â€œ7 is equal to 7.â€ Since 7
= 7, the statement 7
≤
7 is true. (An â€œorâ€ statement is true if either part is
true.)
Note: The statement 7 ≥ 7
is also true.
