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 7³ is written in exponential notation. It means 7 · 7 · 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, “four is less than seven” is written 4 < 7.

Likewise, “seven is greater than four” 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 “negative six is greater than negative two.” 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 “negative five is less than three.”

This is true because -5 lies to the left of 3 on the number line.

c. True. 7 ≤ 7 is read “seven is less than or equal to 7.” This means either “7 is less than 7” or “7 is equal to 7.” Since 7 = 7, the statement 7 ≤ 7 is true. (An “or” statement is true if either part is true.)

Note: The statement 7 ≥ 7 is also true.