Interval Notation
Interval notation is a Grade 7 math skill from Yoshiwara Intermediate Algebra used to express the domain and range of functions or solution sets of inequalities. Students learn to write intervals using brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints, and use ∞ for unbounded intervals.
Key Concepts
Property An interval is a set that consists of all the real numbers between two numbers $a$ and $b$. 1. The closed interval $[a, b]$ is the set $a \le x \le b$. 2. The open interval $(a, b)$ is the set $a < x < b$. 3. Intervals may also be half open or half closed , like $[a, b)$ which is $a \le x < b$. 4. The infinite interval $[a, \infty)$ is the set $x \ge a$. 5. The infinite interval $( \infty, a]$ is the set $x \le a$. A union of intervals, denoted with $\cup$, combines two or more sets.
Examples The inequality $ 4 \le x < 1$ is written in interval notation as $[ 4, 1)$.
The set of all numbers greater than 5 is written as the infinite interval $(5, \infty)$.
Common Questions
What is interval notation?
Interval notation is a compact way to express a set of numbers between two values. Use [a, b] if both endpoints are included, (a, b) if both are excluded, and mix brackets/parentheses as needed.
How do you write x > 3 in interval notation?
x > 3 is written as (3, ∞). The parenthesis shows 3 is excluded, and ∞ always uses a parenthesis.
How do you write -2 ≤ x < 5 in interval notation?
[-2, 5). The bracket at -2 means included; the parenthesis at 5 means excluded.
How is interval notation related to set notation?
Interval notation is a shorthand for a set of real numbers. (a, b) = {x | a < x < b} in set notation.