Whole Numbers - Definition, Natural numbers and Properties

We see numbers all around the globe; they are utilized to count items, represent or exchange money, measure temperature, tell time, and more.

Whole numbers are also considered counting numbers. We will study whole numbers and associated topics in this article. The number system in mathematics consists of all sorts of numbers, such as natural numbers and whole numbers, prime numbers and composite numbers, integers, real numbers, imaginary numbers, and so on, all of which are used to conduct various computations.

Natural numbers are a set of positive integers, and natural numbers, along with zero (0), constitute a set known as whole numbers. On the other hand, Zero is an ambiguous identity that symbolizes a null set or no outcome at all. In layman's terms, whole numbers are a collection of numbers that do not contain any fractions, decimals, or even negative integers. It is a set of positive numbers and zeroes. The primary distinction between natural and whole numbers is the unique number zero. Whole Numbers are the natural numbers plus the number 0. In mathematics, the set of whole numbers is {0, 1, 2, 3, ……. infinite}. The capital number W represents this group of whole numbers.

W = {0, 1, 2, 3, 4, 5, …... 10232, 76687, …… infinite}

We can summarize the concept of whole numbers in the following 4 points

The set of natural numbers comes under the whole numbers.
The whole collection of counting numbers is inside the set of whole numbers.
Zero is included in whole numbers, and the set of whole numbers begins with 0.
All the numbers included inside the whole numbers are real numbers.

Let us now learn a bit about zero and its properties. Whole numbers begin with 0 and go up from there to eternity (from the definition of whole numbers). As a result, 0 is the smallest whole number.

Brahmagupta, a Hindu astronomer and mathematician, defined zero for the first time in 628. In layman's terms, zero is a number on a number line that falls between the positive and negative values. Even though zero has no value, it is used as a placeholder. As a result, zero is neither a positive nor a negative number.

Properties of a Whole Number:

Whole numbers have four basic properties, which are defined below:

Closure property: This property states that if mathematical operations are performed on whole numbers, then the result also remains a positive integer from the set of whole numbers.

Associative property: This property states that the addition or multiplication of any three whole numbers stays the same even if the orientation of the numbers change.

Commutative property: This property states that for any two whole numbers, the addition and multiplication remain the same even if the position of the numbers is interchanged.

Distributive property: According to this property, the multiplication of a whole number is spread thoroughly over the addition of two numbers. This means the result when p is multiplied to (q + r) is equal to the sum of the individual product of p with the terms, i.e., qp + pr.