Equal, Greater, or Less Than

As well as the familiar equals sign (=) it is also very useful to show if something is not equal to () greater than (>) or less than (<)

Equality and Inequality Definition

In mathematics, equality is a relationship between 2 quantities or more (generally 2 mathematical expressions) asserting that the expressions represent the same mathematical object or that the quantities have the same value.

The equality between X and Y is written X = Y, and pronounced X equals Y. The symbol “=” is called an “equals sign”.

An inequality is a relation that holds between 2 values when they are different. The notation x ≠ y means that x is not equal to y. It does not say that one is greater than the other, or even that they can be compared in size.

For values that are elements of an ordered set (such as the real numbers or integers), they can be compared in size. The notation x < y means that x is less than y. The notation x > y means that x is greater than y.

Less Than and Greater Than

The “greater than” sign and the “less than” sign look like a “v” on its side.

To remember which way around the “<” and “>” signs go, just remember:

  • BIG > small
  • small < BIG

… Or Equal To …

Sometimes we know a value is bigger, but may also be equal to!

To show this, we add an extra line at the bottom of the “greater than” or “less than” symbol like this:

The “greater than or equal to” sign:

The “less than or equal to” sign:

All symbols

SignSign meansWhen to useExample
=equalsWhen 2 values are equal1+2 = 3
not equal toWhen 2 values are definitely not equal4+7 ≠ 0
<less thanWhen a value is smaller than another5 < 6
>greater thanWhen a value is bigger than another9 > 8
<Less than or equal toWhen a value is smaller than or equal to anotherBalls > 10
>greater than or equal toWhen a value is bigger than or equal to anotherCats < 11

Combining

We can sometimes say 2 (or more) things on the one line:

Examples

ConditionSignExample
Something greater than 4 and less than 7a < x < b4 < x < 7
Something greater than or equal to 4 and less than 7a ≤ x < b4 ≤ x < 7
Something greater than 4 and less than or equal to 7a < x ≤ b4 < x ≤ 7
Something greater than or equal to 4 and less than or equal to 7a ≤ x ≤ b4 ≤ x ≤ 7

Long Example

ConditionExample
x is greater than 4 and less than 74 < x < 7
7 is less than y7 < y
Combination of condition 1 & condition 24 < x < 7 < y
y is less than 11y < 11
Combination of condition 3 & condition 44 < x < 7 < y < 11

Learn More

Basic Math

Concentric Circles

Ascending & Descending Order

Improper Fractions

Math Definitions

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