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Main types

Natural numbers 

The counting numbers {1, 2, 3, ...}, are called natural numbers. They include all the counting

numbers i.e. from 1 to infinity.

Whole numbers 

They are the natural numbers including zero. Not all whole numbers are natural numbers, but all

natural numbers are whole numbers.

Integers 

Positive and negative counting numbers, as well as zero.

Rational numbers 

Numbers that can be expressed as a fraction of an integer and a non-zero integer. [1]

Real numbers 

 All numbers that can be expressed as the limit of a sequence of rational numbers. Every realnumber corresponds to a point on the number line.

Irrational numbers 

 A real number that is not rational is called irrational.

Complex numbers 

Includes real numbers and imaginary numbers, such as the square root of negative one.

Hypercomplex numbers 

Includes various number-system extensions: quaternions, octonions, tessarines, coquaternions, 

and biquaternions.

Number representationsDecimal 

The standard Hindu–Arabic numeral system using base ten.

Binary 

The base-two numeral system used by computers. See positional notation for information on

other  bases.

Roman numerals 

The numeral system of  ancient Rome, still occasionally used today.

Fractions A representation of a non-integer as a ratio of two integers. These include improper fractions as

well as mixed numbers.

Scientific notation

 A method for writing very small and very large numbers using powers of 10. When used in

science, such a number also conveys the precision of measurement using significant figures.

Knuth's up-arrow notation and Conway chained arrow notation

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Notations that allow the concise representation of extremely large integers such as Graham's

number .

Signed numbers

Positive numbers

Real numbers that are greater than zero.

Negative numbers 

Real numbers that are less than zero.

Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero.

When zero is a possibility, the following terms are often used:

Non-negative numbers

Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero

or positive.

Non-positive numbers

Real numbers that are less than or equal to zero. Thus a non-positive number is either zero or 

negative.

Types of integers

Even and odd numbers 

 A number is even if it is a multiple of two, and is odd otherwise.

Prime number  

 A number with exactly two positive divisors.

Composite number   A number that can be factored into a product of smaller integers. Every integer greater than one

is either prime or composite.

Square number  

 A numbers that can be written as the square of an integer.

There are many other famous integer sequences, such as the sequence of Fibonacci numbers, the

sequence of factorials, the sequence of perfect numbers, and so forth.

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Classification of numbers

The chart below will help you with the classification of numbers a lot. It will makes things crystal clear.

Important observations you need to make from the chart.

Observation #1:

Notice that √(9) is a natural number. It is because √(9) = 3

Observation #2:

Notice that the only difference between natural numbers and whole numbers is the zero.

Whole numbers = Natural numbers + zero

Observation #3:

Notice that the difference between whole numbers and integers are the negative numbers.

Integers = Whole numbers + the negative of the whole numbers

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Observation #4:

 All integers are fractions. Not all fractions are integers

Example: -2 is an integer and can be written as -2/1 to make it a fraction.

However, -1/3 = -0.333333333 is not an integer 

Observation #5:

Fractions can be written as a terminating decimal or a repeating decemal

Example: 1/2 = 0.5 and 0.5 is a terminating decimal. 1/3 = 0.3333333 and 0.3333333 is a repeatingdecimal

Observation #6:

Rational numbers = Integers + fractions

Observation #7:

Irrational numbers are numbers that cannot be written as a fraction

Example: pi= 3.14..., 2.224879566117426874, √(7)

 Another way to see them is that they are neither repeating decimals nor terminating decimals

Observation #8:

Real numbers = rational numbers + irrational numbers

Observation #9:

The difference between complex numbers and real numbers is that complex numbers give solutions for the following expressions and more!

√(-7), √(1-8), √(-25) = 5i, etc..