# Relationship of Inequality

## Relationship of Inequality

Relationship between two quantities of different values.

### Notations

The relationship of inequality is denoted by the symbol “≠”, which is read as “does not equal” or “is not equal to”. The symbol for this relationship is used only between numbers, numerical variables or sets.
The relationship of strict inequality is denoted by one of the following symbols:

• The symbol “>” is read as “is greater than”.
• The symbol “<” is read as “is less than”.

These symbols are used only between numbers or numerical variables.

Included in the symbols used to express inequalities are the following two non-strict inequality symbols:

• x ≤ 9 is read as “four plus is less than or equal to nine”. The solution set of the inequality must include the solution to the equation 4 + x = 9.
• The relationship 4 + x ≥ 9 is read as “four plus x is greater than or equal to nine”. The solution set of the inequality must include the solution to the equation 4 + x = 9.

### Examples

• The relationship 4 + 3 ≠ 9 is read as “four plus three is not equal to nine” or “four plus three does not equal nine”.
• The relationship 4 + 3 < 9 is read as “four plus three is less than nine”.
• The relationship 4 + 10 > 9 is read as “four plus ten is greater than nine”.

### Examples

The symbols “<” and “>” were used for the first time by English mathematician and astronomer Thomas Harriot in his book Artis Analyticae Praxis, which was published posthumously in 1631 and included the first works in modern algebra. Harriot’s inspiration for these symbols came from a symbol he saw on the arm of a North American Indigenous man in 1585. His drawings of the moon as seen through a telescope are the first in astronomy. 