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    What are Natural Numbers? | Definition | List

    Natural numbers are a fundamental set of numbers used for counting and ordering. They are the positive integers, excluding zero. In mathematical notation, natural numbers are often represented by the symbo \( \mathbb{N} \). Exploring the definition and examples of natural numbers offers a deeper understanding of their role in the numerical landscape.

    What are Natural Numbers?

    Natural numbers are the set of positive integers starting from 1 and continuing indefinitely. They are expressed as 1, 2, 3, 4, 5, and so on.

    Natural numbers start with 1 and then continue indefinitely, progressing through the positive integers such as 2, 3, 4, and so on. Zero and negative numbers are not considered natural numbers; they fall into different categories within the number system.

    Examples of Natural Numbers

    A few examples of natural numbers are 22, 52, 73, 9992, 14202, and so on.

    Set of Natural Numbers

    The set of natural numbers, denoted by N, is the collection of all positive integers starting from 1 and extending indefinitely. Mathematically, it can be represented as follows:

    N = {1,2,3,4,5,6,7,8,9,10,…}

    Smallest Natural Number

    The smallest natural number is 1.

    Natural Numbers from 1 to 100

    Here are the natural numbers from 1 to 100

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

    Odd Natural Numbers

    Odd natural numbers are integers greater than zero that are not divisible by 2. In other words, when you divide an odd natural number by 2, you will not get a whole number. The sequence of odd natural numbers starts from 1 and includes every other positive integer.

    For example, 1, 3, 5, 7, 9, 11, and so on, are odd natural numbers. These numbers have the property that when divided by 2, there is always a remainder of 1.

    Even Natural Numbers

    Even natural numbers are integers greater than zero that are divisible by 2. In other words, when you divide an even natural number by 2, you get a whole number without any remainder. The sequence of even natural numbers starts from 2 and includes every other positive integer that is divisible by 2.

    For example, 2, 4, 6, 8, 10, 12, and so on, are even natural numbers. These numbers have the property that when divided by 2, there is no remainder.

    Properties of Natural Numbers

    The properties of natural numbers can be categorized into four main types:

    1. Closure Property
    2. Commutative Property
    3. Associative Property
    4. Distributive Property

    Operations With Natural Numbers

    Operations with natural numbers involve fundamental mathematical actions. Key operations include:

    1. Addition: Combining natural numbers to find their total.
    2. Subtraction: Determining the difference between two natural numbers.
    3. Multiplication: Repeated addition, finding the total of equal groups.
    4. Division: Sharing or grouping natural numbers to find the quotient.
    5. Exponentiation: Raising a natural number to a power.
    6. Root Extraction: Finding the root of a natural number.

    Difference Between Natural Numbers and Whole Numbers

    Property Natural Numbers Whole Numbers
    Definition Positive integers greater than zero. Non-negative integers (including zero).
    Set notation
    Inclusion of zero Excludes zero. Includes zero.

    Solved Examples

    Question 1: What are the first 10 natural numbers?

    The first 10 natural numbers are:

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10

    These numbers form the initial sequence of positive integers, starting from 1 and extending up to 10.

    Question 2: Sort out the natural numbers from the following list: 20, 125, 6.9, 5/2, 60, −78, 0, −2, −3/2

    The natural numbers in the list are:

    20, 125, 60

    FAQs on Natural Numbers

    1. What are natural numbers?
      • Natural numbers are a set of positive integers starting from 1 and extending indefinitely.
    2. Do natural numbers include zero?
      • No, natural numbers do not include zero. They begin with 1 and include all positive integers.
    3. Are negative numbers considered natural numbers?
      • No, natural numbers are exclusively positive integers. Negative numbers are not part of the set of natural numbers.
    4. Is there a largest natural number?
      • No, there is no largest natural number. Natural numbers extend infinitely, and there is no upper limit.
    5. What is the symbol for natural numbers?
      • The symbol for the set of natural numbers is .
    6. Can fractions or decimals be natural numbers?
      • No, natural numbers are whole numbers, and they do not include fractions or decimals.
    7. Are natural numbers used for counting only?
      • While natural numbers are commonly used for counting, they also play a role in ordering, labeling, and representing quantities.
    8. What is the first natural number?
      • The first natural number is 1.
    9. Do natural numbers have an end?
      • No, natural numbers continue indefinitely. There is no endpoint, and the set goes on forever.
    10. Are natural numbers a subset of integers?
      • Yes, natural numbers are a subset of integers. Integers include both positive and negative whole numbers as well as zero.
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