[Maths Class Notes] on What are Natural Numbers? Pdf for Exam

Natural numbers are those numbers which we use to count. A set of natural numbers is typically expressed by the symbol N. Natural numbers for example: N = {1, 2, 3, 4, 5, 6, 7,…}. Natural numbers are also known as counting numbers because they are generally required for counting. For example, to set something in the time, you would use natural numbers to count. These numbers are the number that occurs commonly and obviously in nature. As such, they are whole, non-negative numbers. We often see them portrayed on a number line. Natural numbers, since they are integers, do not have a decimal point.

What is the Definition of Natural Number?

The natural numbers are a base from which many other number sets may be built by expansion: the integers, by including (if not yet in) the neutral component 0 and for each nonzero natural number n there is an additive inverse (−n); the rational integers, by including a multiplicative inverse (1/n) for each nonzero integer n (and also the product of these inverses by integers); the real numbers by including with the rationals the limits of (gathering) Cauchy sequences of rationals; the complex numbers, by including with the real numbers the unsolved square root of minus one (and also the sums and outputs thereof); and so on.

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Is Zero a Natural Number?

The natural number begins from 1 to infinity. Hence, 0 is not a natural number but a whole number with a null value.

Define Natural Number with Example

34, 86, 90, 105, 470, 5090, 100034, etc. are all examples of natural numbers.

So, natural numbers are a set of all the whole numbers excluding 0.

There is one branch of mathematics that matters itself matters with the properties of natural numbers (including natural number-based modular arithmetic). This is the branch known as number theory. Since the time of the ancient Greeks, mathematicians have explored these properties for their well-being and their supposed connections with the supernatural. Besides, in recent times many practical uses, quite apart from counting and computation, have been found for natural numbers and their special properties. The uses include check-digit systems, secret codes, and many other uses.

Properties of Natural Numbers

1. Closure property

2. Commutative property

3. Associative Property

4. Distributive property

Closure Property: Natural numbers are always bound under addition and multiplication. The sum and product of two or more natural numbers will always produce a natural number.

1. Addition: 2 + 4 = 36, 6 + 6 = 12, etc. In every case like this, the resulting number is always a natural number.

2. Multiplication: 2 × 9 = 18, 2 × 4 = 8, etc. Here, in this case also, the resultant is always a natural number.

3. Subtraction: 9 – 2 = 7, 5 – 7 = -2, etc. But in this case, the result may or may not be a natural number.

4. Division: 10 ÷ 2 = 5, 10 ÷ 6 = 1.666, etc. Also in this case, the resultant number may or may not be a natural number.

Commutative Property: Sum and product of natural numbers show the commutative property. Subtraction and division of natural numbers do not display the commutative property.

1. Addition: a + ( b + c ) equals ( a + b ) + c

2. Multiplication: a × ( b × c ) equals ( a × b ) × c

3. Subtraction: a – ( b – c ) not equals ( a – b ) – c

4. Division: a ÷ ( b ÷ c ) not equals ( a ÷ b ) ÷ c

Associative Property: The associative property holds true in case of addition and multiplication of natural numbers i.e. a + (b + c) = (a + b) + c and a × (b × c) = (a × b) × c.

Distributive Property: Multiplication of natural numbers is always distributive above addition. Multiplication of natural numbers is also distributive above subtraction. This property is known as Distributive property.

Solved Examples

Question 1: What are the first ten natural numbers?

Solution: The first ten natural numbers are: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Question 2: Define the whole number.

Answer: Whole numbers are easy to remember. They are not fractions, they are not decimals, they are simply whole numbers. The only difference from natural numbers is that we include the zero when we are referring to whole numbers.