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Type of Numbers

We need to use numbers in order to work in mathematics. A real number is a number used to represent quantities such as price, length, distance etc.

The set of real numbers is in turn made up of different types of numbers viz. Natural, Whole, Integers, Rational and Irrational.

Natural Numbers

In the beginning, “number” meant something you could count, like how many sheep the farmer has. From this evolved the notion of the natural numbers, also called the counting numbers.

Examples of natural numbers are: 1, 2, 3, 4, 5… basically all the numbers used for counting.

This set of natural numbers is denoted by N.

Whole Numbers

The natural numbers together with the number “zero” is called the set of Whole numbers.

Example: 0, 1, 2, 3, 4, 5…

The set of whole numbers is denoted by W.

So the set of whole numbers is basically the set of natural numbers combined with 0.

The set of whole numbers combined with the negative numbers -1,-2,-3… forms the set of integers.

Example: …,-5,-4,-3,-2,-1,0,1,2,3,4,5…

This set is denoted by Z.

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A rational number can be defined as any number that can be expressed as $$ \frac{m}{n}$$ where m and n are both integers and n is not equal to 0.

In other words, rational numbers include repeating decimals, terminating decimals and fractions.

Examples: $$ \frac{2}{3},-3\frac{1}{2},0.6666$$

This set is denoted by R.

Hence, Rational numbers is the combination of integers, whole numbers, natural numbers and all the fractions in between.

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Irrational Numbers

Irrational numbers are defined as numbers that are not rational.

These are basically numbers that cannot be written as fractions or decimals that do not terminate or repeat (a rational will do at least one).

Examples: $$ 0.254787558785785775…… \pi, \sqrt{2}$$ etc.

This set is denoted by Q.

Summary of Number System

We can summarize the set of real numbers by the following diagram.

Real Numbers

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