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 (**<**)

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## 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

Sign | Sign means | When to use | Example |

= | equals | When 2 values are equal | 1+2 = 3 |

≠ | not equal to | When 2 values are definitely not equal | 4+7 ≠ 0 |

< | less than | When a value is smaller than another | 5 < 6 |

> | greater than | When a value is bigger than another | 9 > 8 |

< | Less than or equal to | When a value is smaller than or equal to another | Balls > 10 |

> | greater than or equal to | When a value is bigger than or equal to another | Cats < 11 |

## Combining

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

### Examples

Condition | Sign | Example |

Something greater than 4 and less than 7 | a < x < b | 4 < x < 7 |

Something greater than or equal to 4 and less than 7 | a ≤ x < b | 4 ≤ x < 7 |

Something greater than 4 and less than or equal to 7 | a < x ≤ b | 4 < x ≤ 7 |

Something greater than or equal to 4 and less than or equal to 7 | a ≤ x ≤ b | 4 ≤ x ≤ 7 |

### Long Example

Condition | Example |

x is greater than 4 and less than 7 | 4 < x < 7 |

7 is less than y | 7 < y |

Combination of condition 1 & condition 2 | 4 < x < 7 < y |

y is less than 11 | y < 11 |

Combination of condition 3 & condition 4 | 4 < x < 7 < y < 11 |