Maths - Set Notation for Inequalities
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.