# Difference between Natural and Whole numbers

A number is defined as any mathematical value that is used to measure or count some values. A number is mainly used for mathematical calculations. The number can be of any type like a whole number, natural number, integers, rational number, irrational number, real number, and complex numbers. The decimal system that is mostly used in mathematics is one of the types of Number systems.

### Number System

The number system is defined as the representation of numbers with the use of digits or symbols. It is a system that represents numbers. It basically defines the set of values to be represented as quantity. The numbers used in the number system are used as digits typically ranging from 0 to 9. The number system is a mathematical notation for representing numbers using digits.

**Natural Numbers**

The other name for natural numbers is **counting numbers** as one can count the natural numbers with the use of hands. The natural numbers form a part of the number system which is positive integers from 1 onwards. These numbers are represented on the right side of a number line. The example of natural numbers is 1, 2, 3, 4, 5,…N.

Zero and negative integers are not a part of natural numbers. The smallest natural number ever possible is 1 and the largest natural number can be any infinite positive integer value. Fractions, decimal values, complex numbers, etc are not natural numbers.

Examples of Natural numbers

- 23 is a natural number as it’s a positive integer
- -34 is not a natural number as it’s not a positive integer
- 1.3 is not a natural number as it’s a decimal value.
- 4/5 is not a natural number as it’s a fraction

**Whole numbers**

Whole numbers are defined as numbers that include positive integers along with zero, similar to natural numbers, these numbers are represented on the right side of a number line. The smallest whole number possible is zero and the largest natural number can be any infinite positive integer value. A natural number is a subset of the whole numbers as all the natural numbers are whole numbers but all the whole numbers are not natural numbers exception being zero. Fractions, decimal values, complex numbers, etc are not whole numbers, the example of whole numbers are 0,1, 2, 3, 4, 5,…N. All the arithmetic operations can be performed on the whole numbers such as addition, subtractions, multiplications, etc.

Examples of Whole numbers

- 232 is a whole number as it’s a positive integer
- -314 is not a whole number as it’s not a positive integer
- 1.23 is not a whole number as it’s a decimal value
- 4/15 is not a whole number as it’s a fraction

### Difference between Natural numbers and Whole numbers

Natural numbers and Whole numbers have all the numbers in common except zero and that is the major difference between both of them. This difference makes Natural numbers counting in nature.

Natural numbers | Whole numbers |

The set notation of natural numbers is {1,2,…N} | The set notation of Whole numbers is {0,1,2,…N} |

The smallest natural number is 1 | The smallest natural number is 0 |

All non zero positive integers are a part of natural numbers | All positive integers are a part of whole numbers |

A natural number is a subset of the Whole number | The whole number is a superset of natural number |

Natural numbers are represented by the letter N | Whole numbers are represented by the letter W |

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