INDEX
Complex Numbers
Exponentiation
Algebraic Transformations
Algebraic Equations and Inequalities
Functions
Discrete Algebra
Basic Formulas
Graphics of Basic Functions
Numbers and Sets
Balloon

Introduction

About Algebra

Arithmetic Operations

Addition and Subtraction

Multiplication and Division

Criterions for Divisibility

Real Number System

Types of Numbers

Geometric Interpretation of Real Numbers

Irrational Number

Properties of Real Numbers

Fractions
Proportions

Property of Equal Proportions

Absolute Values

Graphical Illustrations

Sets and Intervals

Sets

Subsets

Operations with Sets

Intervals



Sets
Key Topics Remaining: Intervals

A set is a finite or infinite collection of objects. The objects are called elements or members of a set.
A set is denoted by an upper case letter. A pair of braces is used to enclose elements of the set, separating the individual elements by commas.
For instance,

 A ={ x, a, b, c}. 

The statements   ¨ is an element of the set  A ¨  and   ¨ is not an element of  A ¨  are written symbolically as

,
correspondingly.

A set can be also defined by describing its elements through their characterizing properties. For example, the statement
 ¨ is the set of all elements  x  such that  x  has the property  P ¨
is symbolized as

 A = { x | P },
where symbol  |  is used instead of  ¨such that¨.

A null set (or empty set) has no elements.
Examples
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