Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Elementary Algebra
Topic: Linear Equations and Inequalities
Subtopic: Set and Interval Notation

Overview

An infinite set of numbers (eg. all Real numbers greater than or equal to 1) can be represented in three different ways:

1. Graphing the set on a number line
2. Writing the set in inequality notation, eg. x≥1
3. Writing the set in interval notation, eg. [1,+∞)
When graphing on a number line, watch when to use "open" vs. "closed" circles on the endpoints. Inequality notation is pretty straight forward. Interval notation is the most commonly used method so learn it well.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.4.1 Sketch a solution set on a number line
• 2.4.2 Know the difference, on a number line, between an open and closed circle
• 2.4.3 State a solution set in inequality notation and in the closely related set-builder notation
• 2.4.4 State a solution set in interval notation
• 2.4.5 Know the difference, in interval notation, between the regular parenthesis ( and the square bracket [
• 2.4.6 Know to write intervals in the order of the number line, i.e. with the smaller number on the left

Terminology

Terms you should be able to define: set, solution set, inequality sign, inequality notation, set-builder notation, interval notation, open interval, closed interval

Text Notes

When studying your textbook for this lesson here are a few things to watch.

• Some texts (irritatingly) emphasize set-builder notation over inequality notation. Set-builder is really an expanded form of inequality notation (just extra symbols -- more than necessary IMO). Rather than writing a solution in inequality notation e.g. x ≤ 1, they may use set-builder notation { x | x ≥ 1 } which is read "the set of all x such that x is greater than or equal to 1". The | bar means "such that". Some online testing systems will have you give the answer in set-builder notation, but they may write part of the notation for you as in { x | _____ } and all you have to do is write the inequality notation in the blank.

• The most common notation used especially in later courses is interval notation. Watch the class discussion boards for mini-lessons about this notation. There are several specifics to remember when writing interval notation.