Whole numbers – Definition – Symbol and Examples

What are Whole Numbers

In our number system, various kinds of numbers such as; natural numbers, odd and even numbers, whole numbers, real numbers etc.

In 628 A.D., first time the Indian mathematician and astronomer, Brahmagupta invented the number zero. Zero is used as a placeholder, it has no any value, so zero is neither a positive nor a negative number.

What are Natural Numbers?

The counting numbers, (1, 2, 3, 4, ……..) are  known as “Natural Numbers” or counting numbers.

1, 2, 3, 4, 5… is the set of counting numbers, so the collection of numbers starting from 1 to infinity is called natural numbers.

N = {1, 2, 3, 4, 5…}

Definition:

Example: Set of Whole numbers

W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9…… }

These numbers are positive integers including zero.

Set of Integers Z = {…-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5…}

Whole numbers are a set of numbers, including all natural numbers and zero.

All whole numbers are real numbers, but all real numbers are not whole numbers.

Whole numbers are real numbers that do not contain fractions, decimals or negative values.

(2/3, 6/7, 4.7, 5.9 are not whole numbers)

Whole Number Symbol

3. Whole numbers are denoted by “W” in capital letters.  i.e., W = ( 0, 1, 2, 3, 4, 5, 6,…)

The following figure shows that natural numbers are subset of whole numbers.

The numbers (0, 1, 2, 3, 4, 5, …..) are known as Whole numbers.

Smallest whole Number

Whole Numbers on Number Line

The set of whole numbers can be shown on number line. This is the number line for Whole Numbers.

The whole numbers on the number line are often represented by points.

The distance between points 0 and 1 are is called unit distance.

In this way a number line starting from 0 and marked points at unit distance as 0, 1, 2, 3, 4, 5, ..on the right side line is called whole number line.

Whole Numbers vs Natural Numbers

Every natural number is a whole number.

Every whole number is not a natural number.

Every whole number other than zero is a natural number.

Here are some facts about whole numbers.

1. All natural numbers are whole numbers, but all whole numbers are not natural numbers.

2. The first and smallest whole number is zero.

3. Whole numbers are denoted by “W”.  i.e.

             W = ( 0, 1, 2, 3, 4, 5, ………….)

4. There is no last or greatest whole number.
W = ( 0, 1, 2, 3, 4, 5, …) set of whole numbers.

Thus their is no end of numbers. The system has
infinite numbers.

5. Whole numbers can not be expressed in ngative  form i.e.

-1, -2, -3, -4, -5…….are not whole numbers.

6. Whole numbers can not be expressed in fractional form i.e.

2/3,  8/5,  5/4…….are not whole numbers.

7. Whole numbers can not be expressed in decimal form i.e.
  2.3,  8.5,  5.4…….are not whole numbers.