Properties of Natural Numbers in Maths

In mathematics, the numbers which are used for counting and ordering are called natural numbers. For example- 1) “there are seven tables”. 2) “he is the second tallest person in his class” and so on. In other words, natural numbers constitute positive integers on a number line. Besides, including zero (0) to the natural numbers forms the set of whole numbers on the number line. An English alphabet used for denoting the natural number is N.

 Properties of the natural numbers such as addition, multiplication, subtraction, divisibility and the distribution of numbers can be studied in number theory. All these properties are introduced with the students in their primary and secondary classes, along with suitable examples. The detailed explanations of these properties are given below.

 Closure property of natural numbers says that the addition and multiplication of natural numbers again result in a natural number only. If the sum or multiplication of numbers in any order gives the same result, then it is called commutative property of natural numbers. Similarly, natural numbers also hold true for associative and distributive properties. The associative property is true for addition and multiplication in case of natural numbers, whereas distributive property holds true for natural numbers of multiplication over addition.

 Existence of identity elements in the number system also adds two more properties with respect to the natural numbers. We know that in mathematics, an identity element is a special type of element of a set, which leaves any element of the set unchanged when combined using binary operations with it. If we add zero (0) to any natural number, the result is the number itself. Hence, zero is called the additive identity for natural numbers.

 Similarly, when we multiply any natural number with one (1), the result is the number itself and hence, 1 is called the multiplicative identity. In other words, the multiplication of a number with its reciprocal or multiplicative inverse is equal to unity. Some of these properties are applicable to integers, whole numbers and rational numbers. Thus, we can conclude that natural numbers are closed, commutative, associative under addition and multiplication. Also, there exist multiplicative and additive inverses for every natural number.