About natural number

Aug 09, 2022, 16:45 IST

What are Natural Numbers?

The natural numbers are part of the number system that includes all positive integers from 1 to infinity and are also used for counting purposes. It does not include zero (0). In fact, 1,2,3,4,5,6,7,8,9…. also called counting numbers. The natural numbers are part of the real numbers that include only positive integers, i.e., 1, 2, 3, 4, 5, 6, ………. except zero, fractions, decimals, and negative numbers.

Note: Natural numbers do not include negative numbers or zero.

In this given article, you will learn more about natural numbers, their definition, comparison with whole numbers, representation on a number line, properties, etc. Counting numbers are known as natural numbers. We always start counting anything from 1 always. So natural numbers start from 1. For More Mathematics Doubts visit main page of Physics Wallah.

Natural Numbers Definition

As explained in the introductory section, natural numbers are numbers that are positive integers and include numbers from 1 to infinity (∞). These numbers are countable and are generally used for calculation purposes. The set of all natural numbers represents the letter "N."

N = {1,2,3,4,5,6,7,8,9,10…….}

Examples: 23, 56, 78, 999, 100202, and so on.

Set of Natural Numbers

A set is a collection of elements (number). The set of natural numbers in mathematics is written as {1,2,3,...}. The N symbol denotes the set of natural numbers. N = {1,2,3,4,5,...∞}

Odd Natural Number

Odd natural numbers are odd numbers belonging to the set N. So the set of odd natural numbers is {1,3,5,7,...}.

Even Natural Number

Even natural numbers are numbers that are even, Which are exactly divisible by 2 and belong to the set N. So the set of even natural numbers is {2,4,6,8,...}.

Natural Numbers and Whole Numbers

A set of whole numbers is the same as the set of natural numbers, except that it contains another number, 0. In mathematics, the set of integers can be written as {0,1,2,3,...}. It is denoted by the letter W.

W = {0,1,2,3,4…}

From the given definition, we can understand that every natural number is an integer. Also, any integer other than zero is a natural number. Therefore, we can say that the set of natural numbers is a subset of the whole number set.

Difference Between Natural Numbers and Whole Numbers

Natural Numbers on Number Line

The set of a whole number and natural numbers can be shown on a number line, as shown below. All positive integers or integers to the right of 0 are natural numbers, while all positive integers together with zero are the whole number.

Properties of Natural Numbers

Properties of Natural number are given below

• Closure property
• Commutative property
• Associative property
• Distributive property

Closure property

Natural numbers are permanently closed under addition and multiplication. Adding and multiplying two or more natural numbers constantly gives a natural number. In the case of division, subtraction and natural numbers do not obey the closure property, which means that subtracting or dividing two natural numbers may not result in a natural number.

• Addition: 3 + 4 = 7, 1 + 2 = 3 etc. A resulting number is always a natural number in each of these cases.
• Multiplication: 5 × 4 = 20, 2 × 3 = 6 etc. The resultant is always a natural number.
• Division: 10 ÷ 3 = 3.33, 10 ÷ 5 = 2 etc. The resultant may or may not be a natural number.
• Subtraction: 3 – 5 = -2, 9 – 5 = 4 etc. The resultant may or may not be a natural number in these cases.

Commutative property

• Multiplication and Addition of natural numbers show the commutative property. For example, x + y = y + x and a × b = b × a
• Subtraction and division of natural numbers do not show the commutative property. For example, x – y ≠ y – x and x ÷ y ≠ y ÷ x

Associate Property

The product or sum of any three natural numbers remains the same even if the grouping of the numbers changes. This property applies to multiplication and addition but not to division and subtraction.

• Associative property of addition: a + (b + c) = (a + b) + c = 3 + (4 + 1) = 3+ 5 = 8 and the same result is obtained in (3 + 4) + 1 = 7 + 1 = 8
• Associative property of multiplication: a × (b × c) = (a × b) × c = 3 × (4 × 1) = 3 × 4 = 12 and the same result is obtained in (a × b) × c = ( 3 × 4) × 1 = 12 × 1 = 12

Distribute Property

The distributive property is the distributive law of multiplication over addition and subtraction. It states that an expression given in the form a (b + c) can be solved as a × (b + c) = ab + ac. This distributive law, which also applies to subtraction, is expressed as a (b - c) = ab - ac. This means that the operand 'a' is distributed between the other two operands.

• Addition distribution property : a × (b + c) = (a × b) + (a × c)
• Multiplication over subtraction distribution property : a × (b − c) = (a × b) − ( a × c)

Natural Numbers Examples

Q1. Find the natural numbers among the following: -1, 0, 3, 1/2, 5.

Ans. The set of natural numbers in Maths is the set {1, 2, 3, ...}. Now, -1 is a negative number, so it is not a natural number. 0 is also not a natural number. 1/2, being a fractional number, is not a natural number, either. Therefore, among the given numbers, the natural numbers are 3 and 5.

Q2. State true or false according to natural numbers.

1. All natural numbers are whole numbers.
2. 0 is a natural number.
3. All natural numbers are integers.

Ans.

1. True, all natural numbers are whole numbers.
2. False, 0 is not a natural number.
3. True, all natural numbers are integers.

Frequently Asked Question (FAQs)

Q1. Is 23 a Natural Number?

Ans. It is a positive number used in counting. So, yes, 23 is a natural number.

Q2. Is 0 a Natural Number?

Ans. Natural numbers start from 1 and can be written as 1, 2, 3, 4, 5, etc. However, 0 falls under the category of integers and integers. No, 0 is not a natural number.

Q3. Write the first natural number.

Ans. The first ten natural numbers on the number line are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

Q4. How many Natural Numbers are there?

Ans. It is counting numbers that start from 1 and go on till infinity. Therefore, there are infinite natural numbers.