Natural Numbers

Natural numbers can be described as a subset of the integer numbers and have ideological and historical value as they are commonly used for counting and are often seen to have ethnocultural implications. In addition to this, natural numbers are widely used as the elemental blocks for different other number systems involving rational numbers, integers as well as real numbers. These numbers are used for ordering and counting. In simple words, they can be described as words that are utilized for counting cardinal numbers, or words that are utilized for the order that is ordinal numbers. 

What are natural numbers? 

To answer the question of what are natural numbers, the concept of numbers is very important. Natural numbers can be explained as a part of the entire system of numbers which includes positive integers starting from 1 up to infinity. Hence, these are also used for counting. It does not involve the number 0. In this context, it should be stated that natural numbers are often referred to as counting numbers.  Natural numbers are a subset of integers which is again a subset of real numbers involving 1, 2, 3, 4, 5, ….. excluding decimals, fraction, zero, negative, and fraction. 

Definition of Natural Numbers

As discussed previously natural numbers are defined as particularly those numbers that are positive integers and involve numbers starting from 1 up to infinity. These numbers can be counted as well as ordered and are normally used for calculation. This specific set of natural numbers is generally symbolized by the number N. 

N = (1, 2, 3, 4, 5, …..)

Every Natural number is a whole number

To understand that every natural number is a whole number we first need to understand the concept of the whole number. Whole numbers are mostly described as the set of all positive integers incorporating zero. These are a subset of real numbers and do not necessarily involve decimals, negative numbers, or fractions. Sometimes counting numbers is also regarded as whole numbers. 

Hence from the definition of the whole number itself, it is clear that every natural number is a whole number. This means that every natural number is a whole number but every whole number is not a natural number since a natural number doesn’t involve 0. 

In a few words, this can be expressed in the following manner

• Natural numbers are given by {1 – ∞}
• Whole numbers are given by {0 – ∞}

Natural Number properties

Natural numbers have many important properties which can be mostly categorized under four main categories.  These have been outlined in the following

• Commutative property: Both multiplications, as well as addition, show the commutative property. For instance, m + n = n + m shows the additive commutative property whereas m * n = n * m shows the multiplicative commutative property. In this context, it should be mentioned that division and subtraction do not represent the commutative property. For instance m – n ≠ n – m. Further m ÷ n ≠ n ÷ m.
• Closure Property: Here it is important to note that if natural multiplication and addition are considered then natural numbers always satisfy the closure property. The multiplication, as well as the addition of a natural, will always provide a natural number. However, if division or subtraction is considered then the closure may not be obeyed. 
• Distributive Property: Natural numbers satisfy the distributive property both for subtraction as well as addition. In case of subtraction it is given as m * (n – p) = mn – mp whereas in case of addition it is given as m * (n + p) = mn + mp. In simple words multiplication of different natural numbers is distributive over both subtractions as well as addition. 
• Associative Property:  Natural numbers satisfy the associative property in the case of both multiplication as well as addition. These can be demonstrated as “m + (n + p) = (m + n) + p” as well as “m * (n * p) = (m* n) * p” On the contrary, Natural numbers do not satisfy associative law with respect to division as well as subtraction. 

Conclusion 

In this article, the subject of Quantitative aptitude has been mostly discussed. Within this vast subject, the concept of natural numbers has been mostly analyzed. Firstly what mathematicians mean by natural number has been identified which has been followed by its definition. Next discussions have been done on the whole number as well as the natural number and this has been followed by different properties of the natural number.