Number System in Mathematics with Example

Introduction 

 A Number is a mathematical value used for counting and measuring objects and for performing arithmetic calculations. There are different Number Systems like Natural Numbers, Whole Numbers, Integers, Rational Numbers and Irrational Numbers and so on. Similarly there are different categories of Numbers System like Binary Numbers, Decimal Numbers, Octal Numbers, Hexa-Decimal Numbers etc. Let's Explain all Numbers Systems in detail.

Natural Numbers

Natural Numbers are most basic types of numbers that range 1 to infinity. These Numbers are also called Positive Numbers or Counting Numbers. Natural Numbers are represented by symbol N. 

Example:  1, 2, 37, 59, 105, 110, 503, 750 etc.

Whole Numbers

Whole Numbers are basically Natural Numbers, But they also include 0 (zero) number. 

Example:  0, 1, 2, 37, 59, 105, 110, 503, 750 etc.

Integers

Integers are collection of whole numbers plus the negative value of Natural Numbers. Range of Integers is from infinity at the negative end to infinity at the positive end.

Example: -45, -32, -12, -5, 0, 5, 10, 55, 74 etc.

Rational Numbers

The Number which can be written in the form : ^p/_q  where p and q are integers and q ≠ 0, is called Rational Numbers.  For Example : -²/₃ , ⁴/₇ , ³/₅ , 4 , 7 etc.  Here 4 and 7 are also Rational Numbers because it can be written in the form of   ^p/_q . We can write it as ⁴/₁ or ⁷/₁  .

Example:  -¹/₅ ,-²/₃ , ⁴/₇ , ³/₅ , 4 , 7 etc.

Irrational Numbers

A Number called irrational , if it is cannot be written in the form of  ^p/_q  , where p and q are integers and q ≠ 0. You already know that there are infinitely many rational numbers. It turns out that there are many irrational numbers too. Some Examples are...

Example:  √2 , √3, √15,  π , 0.10110111011110...