How can we use the concept:
Intervals are indicated with brackets or parentheses and often look similar to ordered pairs but an interval is showing an inequality or a system of inequalities.
Symbols seen in interval notation can include: brackets [ ] or parentheses ( ); all of the inequality symbols ≤, ≥, <, <; infinity or negative infinity ∞, -∞; equal to or not equal to =, ≠, the union symbol ∪; or the intersection symbol ∩.
Brackets are used to show “less than or equal to” or “greater than or equal to” and parentheses are used to show “less than” or “greater than”. Brackets and parentheses can both be used in one interval.
Some other symbols you might see used in inequalities:
Brackets are used to show “less than or equal to” or “greater than or equal to” and parentheses are used to show “less than” or “greater than”. Brackets and parentheses can both be used in one interval.
Some other symbols you might see used in inequalities:
⋹ means an element is part of a set.
∉ means an element is not part of a set.
∉ means an element is not part of a set.
Sample Math Problems
1. Give the interval notation for x ≤ 7.
Solution:
(-∞,7]
The left side has to have parentheses because we can’t actually equal infinity. And the right side has a bracket indicated by the “less than or equal to”.
(-∞,7]
The left side has to have parentheses because we can’t actually equal infinity. And the right side has a bracket indicated by the “less than or equal to”.
2. Give the interval notation for 0 < x < 4.
Solution:
Solution:
[0, 4)
The bracket indicated “greater than or equal to” while the parentheses indicated “less than” the variable.
3. Give the interval notation for x ≤ - 2 or x < 3
Solution:
x ≤ -2 would be (-∞,-2), we won’t use a bracket here since we can’t actually equal infinity.
x < 3 would be (-∞, 3)
The “or” tells us to use the union symbol.
(-∞, -2) ∪ (-∞, 3)
4. Give the interval notation for x < 5 or x ≥ -5.
Solution:
x < 5 would be (-∞, 5)
x ≥ -5 would be [-5, ∞)
(-∞, 5) [-5,∞ )
