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What is the difference between Integers, whole numbers, and natural numbers?

  • Last Updated : 03 Sep, 2021

Number System, any of various sets of symbols and therefore the rules for using them to denote numbers, which are wont to state what percentage objects are there during a given set or in other words Number system is a mathematical presentation of numbers of a given set. Let’s look at the different types of numbers in the decimal number system,

Types of numbers

There are different types of numbers in the number system, complex numbers include all types of numbers, both real and imaginary, in real numbers, there are rational and irrational numbers. There are integers that go from negative infinity to positive infinity, the integers that go from 0 to positive infinity are whole numbers, the integers that generate from 1 and go up to infinity are natural numbers.

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Integers 



If a set of all-natural numbers are constructed, whole numbers, and negative numbers then such a set is called an Integer set. It can be positive, negative, or zero. For Example : 2 , 5 , -9 , -17 , 112 , etc.

Rational Numbers 

A rational number can be defined as any number which can be represented in the form of p/q where q is greater than 0. For Example 2/5, 22/7, 4/3, etc.

Whole Numbers 

The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity. These numbers exist in the number line. Hence, they are all real numbers. The complete set of natural numbers alongside ‘0’ are called whole numbers. Whole numbers are 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , …

Natural Numbers 

Natural numbers are a part of the number system which includes all the positive integers from 1 to infinity. Natural numbers are 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , …

Difference between Integers, whole numbers, and natural numbers  

The most basic difference between whole numbers and natural numbers is that whole numbers include 0 and natural numbers generate from 1 and therefore do not contain 0. However, Integers include numbers from negative infinity to positive infinity. Below are the point showing major difference between Integers, whole numbers, and natural numbers,



  • For Integers, counting starts from negative infinity, in natural numbers counting starts from 1 while in whole numbers counting starts from 0.
  • It can be said that each one natural numbers are whole numbers but all whole numbers are not natural numbers. However, all natural and whole numbers are Integers but not vice versa.
  • For Example : {-∞,…-1, 0, 1, 2,….+∞} is a set of Integers, {0, 1, 2, 3, 4,…} is a set of whole number while {1, 2, 3, 4,…} is a set of natural numbers.
  • The integers are represented as I, natural numbers are represented as N, whole numbers are represented as W.

W = {I} – {-∞, ….-1}

N = {W} – {0}

Sample Problems

Question 1: Can we say that 7 is both whole number and natural number?

Answer:

Yes, 7 is both whole number and natural number.

Question 2: State whether the given statement is true or false: “all natural numbers are whole numbers”?

Answer:

True, all natural numbers are whole numbers but not vice versa.

Question 3:  Is 5 a whole number and a natural number?

Answer:  



Yes, 5 is both a natural number and whole number.

Question 4: Is 0.7 a whole number?

Answer: 

No, it is a decimal.

Question 5: “-17” is whole number or natural number ?

Answer: 

No, -17 is neither natural number nor whole number.

Question 6: Categorize the given numbers in among Integers, whole numbers and natural numbers,

-3, 77, 34.99, 1, 100

Answer:

NumbersIntegersWhole numbersNatural numbers
-3yesnono
77yesyesyes
34.99nonono
1yesyesyes
100yesyesyes
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