 # Whole Numbers

### What Do You Mean By Numbers?

A number system is known as a number writing system. It is the mathematical notation, which frequently uses numbers or other symbols to describe a certain set. It provides a unique representation of each number and the arithmetic and algebraic structure of the figures. It also allows us to perform arithmetic operations like addition, subtraction and division. Let us now know in this article about the meaning and properties of whole numbers.

### Whole Numbers Definition:

The whole numbers are the number without fractions, and they are a collection of positive integer numbers and zero. It is shown as ‘W’ and the number set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…………}.

Including zero, all figures are true and do not include either fractional or decimal sections i.e. 3/4, 2.2 or 5.5 are not entire quantities.

Furthermore, with all the numbers, subtraction, multiplication and division operations are necessary.

If you are in trouble again, what is an actual amount in mathematics? The accompanying explanation offers a more comprehensive understanding of the whole count:

An integer that is 0 and greater is a whole sum. The first five numbers in all were 0, 1, 2, 3 and 4. They all go up to infinity.

Whole numbers are almost the same as natural numbers except for 0. A whole number, as the name implies, is not a fraction. This cannot be pessimistic either. Since integer numbers range from negative infinity to positive infinity, total numbers are a subset of integer numbers.

The whole number set is expressed by using the basic mathematical definition of a set W = {0, 1, 2, 3,…..} as a collection of objects that share a well-defined property. Beginning with 0, the element x of the set number is created by adding the number before x to its predecessor, which is x-1. Use an ellipsis (...) in braces implies the number of elements in the set is not finite (i.e., infinite).

With the exception of 0, every number x has precisely one immediate predecessor — the amount that falls before x. Each number y has exactly one immediate counterpart — the number after y.

An interesting feature of the whole set of numbers is that there is no largest whole amount. Suppose b is the highest whole number, so b + 1 is a whole number. Nevertheless, b + 1 is greater than b. This approach reveals that you can always find a bigger whole number.

### Whole Numbers Properties:

Complete number properties are based on mathematical operations such as combining, subtracting, splitting and multiplying. If inserted, subtracted or combined; two whole numbers may bring the entire number itself. As a result, we can also get a fraction in the division method.

### Closure Property:

Through combining or dividing, they can be removed, i.e. if x and y are two entire numbers then x × y or x + y is an entire number, too.

Commutative Property of Addition and Multiplication:

The sum and product of any of the two whole numbers are the same regardless of the order in which they are added or multiplied, i.e. if x and y are two full numbers x + y = y + x and x × y = y × x.

If an integer is applied to 0, its value remains unchanged, i.e. when x is an integer then the equation can be written as:

x + 0 = 0 + x.

### Multiplicative Identity:

If an integer is compounded by 1, its value remains constant, i.e. when x is an integer then the equation can be written as:

x × 1 = 1 × x = x

### Associative Property:

When adding or multiplying whole numbers 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 full numbers then the equation can be expressed as:

x + (y + z) = (x + y) + z

And,

x · (y · z) = (x · y) · z

### Distributive Property:

When x, y and z are three complete digits, the multiplication over distributive property is given by:

x × (y + z) = (x × y) + (x × z)

Likewise, the multiplication over subtraction distribution property is given by:

x × (y - z) = (x × y) - (x × z)

### Can Whole Numbers be Negative?

The whole number cannot be negative! The reason for the same has been stated below:

As per the definition of whole numbers, the number line as stated {0, 1, 2, 3, 4, 5, 6... till positive infinity} are constituted in the whole numbers line.

There is no place for negative numbers in the whole numbers line.

### Is 0 a Whole Number?

The set of numbers contains all the Natural Numbers, along with Zero. So yes, 0 (zero) is not only a whole number but it is also the first whole number.

Multiplication by Zero:

By adding a whole number to 0, the answer will always be 0, i.e. x × 0 = 0 × x = 0.

Division by Zero:

The whole number division by 0 is not specified, i.e. when x is a whole number, x/0 is not described.

### Some Facts About the Whole Numbers:

1. There is no single number that can be called ‘big’.

2. Besides 0, all values have an immediate predecessor or a number which falls before them.

3. There is a decimal number or a percentage for two whole quantities, but not whole numbers.

Difference between Whole Numbers & Natural Numbers can be shown in the tabular form as:

## Difference Between Whole Numbers and Natural Numbers:

 Whole Numbers Natural Numbers Whole numbers are:(0, 1, 2, 3, 4, 5, 6...) Natural Numbers are:(1, 2, 3, 4, 5, 6...) The counting of whole numbers starts from the number ‘0’. The counting of natural numbers starts with the number ‘1’. All the numbers on the whole numbers line are not natural numbers. All the numbers on the natural numbers line are whole numbers.

Below figure will help us to understand the difference between the whole number and natural numbers:

Whole Numbers and Natural numbers on Number Line is depicted above.

### Whole Numbers Numerical:

The following are the numerical examples through which you can gain complete knowledge about the whole numbers and how to differentiate between the whole numbers and natural numbers:

Example Number 1:

Are the numbers 100, 227, 198, 4321 whole numbers?

Solution:

Yes, the numbers 100, 227, 198, 4321 are all whole numbers.

Example Number 2:

Solve the equation of: 10 × (5 + 10) using the distributive property.

Solution:

The whole numbers have following distributive properties:

= $x\times \left ( y +z \right ) = \left ( x \times y \right ) + \left ( x\times z \right )$

= $10\times \left ( 5 +10 \right ) = \left ( 10 \times 5 \right ) + \left ( 10\times 10 \right )$

= 50 + 100 = 150

= 10 × (5 + 10) = 150