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Interval Notation

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Interval Notation

Study Guide

Key Definition

Interval notation is a way of writing subsets of the real number line. For example, a closed interval is written as $[a, b]$ and an open interval as $(a, b)$.

Important Notes

A closed interval includes its endpoints: $[a, b]$
An open interval does not include its endpoints: $(a, b)$
Half-open intervals: $[a, b)$ or $(a, b]$
Use set union to combine intervals: $[a, b] \cup (c, d)$
Intervals can represent parts of the number line

Mathematical Notation

$[a, b]$ represents a closed interval

$(a, b)$ represents an open interval

$[a, b)$ or $(a, b]$ represents a half-open interval

$\cup$ is the set union operator

Remember to use proper notation when solving problems

Why It Works

Interval notation provides a concise way to express ranges of values on the real number line using brackets and parentheses.

Remember

Closed brackets $[ ]$ include endpoints; parentheses $( )$ do not.

Quick Reference

Closed Interval:$[a, b]$

Open Interval:$(a, b)$

Set Union:$A \cup B$

Understanding Interval Notation

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Interval notation uses brackets and parentheses to specify which numbers are included in a range. E.g., $[a, b]$ includes $a$ and $b$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a closed interval?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $x$ hours to complete your homework before bedtime, where $x \leq 3$. Write this in interval notation.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the set $[0, 2) \cup (2, 5]$. What numbers are not included in this set?

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following represents the interval $(-\infty, -1] \cup (0, \infty)$?

Recap

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Review key concepts and takeaways