The term "natural numbers" is used to refer to the numbers that are used for purposes of counting (for example: there are ten plates in the kitchen) and for purposes of ordering (for example: this is the second largest mountain in the world).
We can define Natural numbers in many ways:
- Natural numbers are a set of all the whole numbers excluding 0.
- Natural numbers include all positive numbers from 1 to infinity.
- They are a part of real numbers including only the positive integers, but not zero, fractions, decimals, and negative numbers.
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What is the smallest natural number?
The smallest natural number is 1.
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Natural numbers on Number Line
All the positive integers or the integers on the right-hand side of 0 represent the natural numbers.
Properties
The four operations: addition, subtraction, multiplication, and division on natural numbers, lead to four main properties of natural numbers as given below:
- Closure: The sum and product of two natural numbers is always a natural number. This property applies to addition and multiplication but is not applicable to subtraction and division. For example:
1 + 2 = 3. The sum of two natural numbers 1 and 2 is a natural number that is 3.
4 × 8 = 32. The product of two natural numbers 4 and 8 is a natural number, 32.
- Associativity: The sum or product of more than two natural numbers remains the same even if the grouping of numbers is changed. This property applies to addition and multiplication but is not applicable to subtraction and division. For example:
1 + 2 + 3 = 3 + 2 + 1 = 6. The order of addends 1, 2, and 3 does not affect the result.
4 × 2 × 3 = 3 ×2 × 4 = 24. The order of multiplicands 4, 2, and 3 does not affect the result.
- Commutativity: The sum or product of two natural numbers remains the same even after interchanging the order of the numbers. This property applies to addition and multiplication but is not applicable to subtraction and division. For example:
1 + 3 = 3 + 1 = 4. The order of addends 1 and 3 does not affect the result.
2 × 8 = 8 × 2 = 16. The order of multiplicands 2 and 8 does not affect the result.
- Distributivity: The distributive property is known as the distributive law of multiplication over addition and subtraction.
distributive property of multiplication over addition is a × (b + c) = (a × b) + (a × c). For example, 2 × (3 +5) = 2 × 3 + 2 × 5
distributive property of multiplication over subtraction is a × (b − c) = (a × b) − (a × c). For example, 5 × (5−2) = 5 × 5 − 5 × 2
