### 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
*x*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.