Whole Numbers

In this article, we will learn about whole numbers. How are whole numbers different from natural numbers? We will also try and understand various properties of whole numbers.

 

Natural Numbers

The regular numbers are essentially the numbers you initially learned – the numbers you tally with. A few mathematicians consider 0 a characteristic number and others begin at 1. The common numbers are what you would use to check items, for example, the chocolate contributes a treat or the general population in front of you in the thrill ride line comes under natural numbers. The general population in front of you in the line may appear as they go on perpetually; obviously, they don’t generally. The characteristic numbers, in any case, do go on until the end of time. While you can include them hypothesis, you could never be finished.

 

Whole Numbers

They are a group of numbers that includes numbers(0,1,2,3,4,5,6……). These numbers are positive including zero and do not include fractional or decimal parts (\(\frac{3}{4}\),, 2.2 and 5.3 are not whole numbers).

A more comprehensive understanding of the whole numbers can be obtained from the following chart:

Number System

We can have clear idea that what is the difference between whole numbers and natural numbers by the following figure.

Whole and Natural Numbers on Number Line

Properties of whole numbers :

  1. Closure Property: They can be closed under addition and multiplication, i.e., if x and y are two whole numbers then x*y or x+y is also a whole number.
  2. Commutative Property of Addition and Multiplication: The sum and product of two whole numbers will be same whatever the order they are added or multiplied in, i.e., if x and y are two whole numbers x+y=y+x and x*y=y*x
  3. Additive identity: When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number then x+0=0+x=x
  4. Multiplicative identity: When a whole number is multiplied by 1, its value remains unchanged, i.e., if x is a whole number then x*1=1*x=x
  5. Associative Property: When whole numbers are being added or multiplied as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y and z are whole numbers then x+(y+z)=(x+y)+z and x*(y*z)=(x*y)*z
  6. Distributive Property: If x,y and z are three whole numbers, the distributive property of multiplication over addition is x*(y+z)=(x*y)+(x*z), similarly the distributive property of multiplication over subtraction is x*(y-z)=(x*y)-(x*z)
  7. Multiplication by zero: When a whole number is multiplied to 0, the result is always 0, i.e., x*0=0*x=0
  8. Division by zero: Division of a whole number by o is not defined, i.e., if x is a whole number then x/0 is not defined.


Practise This Question

Ted was now curious to find the largest number. He asked 1, “Who is the largest number here?” 1 replied, “I don’t know, ask 2.”
Ted went to 2 who told him to ask 3. Similarly, every number asked Ted to ask the next greater number. After asking a lot of numbers he realized: