# Maths - Set Notation for Inequalities

> Source: https://ollybritton.com/notes/a-level/maths/topics/set-notation-inequalities/ · Updated: 2020-11-02 · Tags: maths, school, year-1

##### What does the set $\{x \colon x < 6.5\}$ describe??
All numbers that are less than $6.5$.

##### What does the set $\{x \colon x > -2\}$ describe??
All numbers that are greater than $-2$.

##### How could you write the set for all numbers less than or equal to $5$??
$$
\{ x \colon x \le 5 \}
$$

##### How could you describe $-2 \le x < 6.5$ as _one_ set??
$$
\{ x \colon -2 \le x < 6.5 \}
$$

##### How could you describe $-2 \le x < 6.5$ as the intersection of _two_ sets??
$$
\{ x \colon x > -2 \} \cap \{ x \colon x < 6.5 \}
$$

##### How can you describe two inequalities that have been "stuck" together using set theory??
The intersection of two sets ($\cap$) for each condition.

##### How can you describe two inequalities that are seperate and can't be combined using set theory??
The union of two sets ($\cup$) for each condition.

##### What should you always do when working with multiple inequalities??
Draw a number line.

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