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



Types of Numbers
Key Topics Remaining: Geometric Interpretation of Real Numbers » Properties of Real Numbers » Fractions » Absolute Values » Sets » Intervals
Natural Numbers:
(For animation, put the pointer anywhere around a figure.)
Integers:     
Note that any natural number is also integer.

Even numbers are divisible by 2.
If  m  is an integer, then  n  = 2m  is an even number.
Examples of even numbers:  2,  4,  6,  8, ....

Odd numbers are leaving a remainder of 1 when divided by 2.
If  m  is an integer, then  n = 2+ 1  is an odd number.
Examples of odd numbers:  1,  3,  5,  7, ...

A number is called a rational number, if it can be written as a quotient of two integers,  p  and  q.

Note that any integer can be written as a quotient of the integer itself and 1. So integers are also rational numbers.

A rational number can be also represented by a terminating decimal or a recurring decimal, for instance,

An irrational number can be represented by non-repeating and non-terminating decimal. It is not capable of being expressed exactly as a ratio of two integers.
Examples of irrational numbers:

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The rational and irrational numbers form together the set of real numbers.

The number zero is used as the origin, and any numbers can be compared with zero.

A positive number  a  is greater than zero,  a > 0.
A negative number  a  is greater than zero,  a < 0.


Examples
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