Natural Number and Whole Number

What are natural numbers?

In mathematics, The Natural numbers are also termed counting numbers, they are all numbers ranging from 1 to infinity. To put it another way, natural numbers are all positive integers from 1 to infinity. Natural Numbers are a subset of Real Numbers that include only positive integers, such as 1, 2, 3, 4, and so on, but not zero, fractions, decimals, or negative numbers.

They are positive integers that range from 1 to infinity. These are the numbers we normally count in our daily lives. Fractions, decimals, negative numbers, and zero are not considered natural numbers. The letter ‘N’ represents the set of Natural Numbers.

• Smallest natural number: The set of natural numbers begins with 1. Therefore, the smallest value of the natural number is 1.

• Set of natural numbers: The set of natural numbers starts with 1 and goes up to infinity.

Whole number: Whole numbers are a collection of numbers that includes all-natural numbers as well as 0. They are real numbers that do not contain fractions, decimals, or negative values. Whole numbers are also considered as counting numbers. In this post, we will study everything there is to know about whole numbers.

Smallest whole number: Whole numbers begin with 0 and go up from there (from the definition of whole numbers). Therefore, 0 is the smallest value of the whole number.

Natural number vs the whole number: Students may ask, “Is Every Natural Number a Whole Number?” To answer these questions, we have to understand the distinction between Natural Numbers and Whole Numbers.

Natural numbers are numbers that range from one to infinity. Whole Numbers, on the other hand, begin at zero and go indefinitely.

As a result, while every natural number is a Whole number, not every whole number is a natural number. Zero is a whole number, not a natural number.

Set of the whole number: The set of the whole numbers begins with 0 and goes up to infinity.

Properties of natural numbers

• Closure Property: The addition and the multiplication of two or more two natural numbers give the results in a natural number. Natural numbers, on the other hand, do not respect the closure principle when it comes to subtraction and division. As a result, subtracting or dividing two natural numbers may not result in a natural number.

for addition and multiplication: – 2+2=4, 3×4=12. Therefore, the addition and multiplication of two natural numbers are also natural numbers.

• Associative Property: The associative property is true for natural number addition and multiplication. That is, even if the order of the numbers is changed, the sum or product of any three natural numbers remains constant. The associative property, on the other hand, does not apply to natural number subtraction and division.

Example- addition- 2+(3+5)=(2+3)+5=8

Multiplication- 3x(4×2)= (3×4)x2=24

• Commutative Property: The addition and multiplication of natural numbers demonstrate the commutative property in the instance of the commutative property. Subtraction and division of natural numbers, on the other hand, do not exhibit the commutative property.

Example- addition – 2+3=3+2=5

Multiplication 4×3=3×4=12

• Distributive Property: Multiplication of natural numbers is always distributive over addition in the case of the distributive property. Furthermore, natural number multiplication is distributive over subtraction.

Example- 2x(3+5)= 2×3+2×5

Properties of the whole number

• Closure Property: The product and sum of two whole numbers are always whole numbers. For example, 5+6=11 (whole number), 8×5=40  (whole number).

• Associative Property: Even if the order of the numbers is modified, the sum or product of any three whole numbers remains constant. For example, adding the following integers has the same result: 8+(3+6) equals (8+3)+6 equals (8+6)+3 equals 17. Similarly, no matter how the numbers are organized, multiplying them yields the same result: 7x(2×5)=(7×2)x5=70

• Commutative Property: Even after switching the order of the numbers, the sum and product of two whole numbers stay the same. This feature asserts that changing the order of addition has no effect on the sum’s value. Let’s say ‘a’ and ‘b’ are both whole numbers. The commutative property states that a + b = b + a. For instance, if a = 7 and b = 12, 7 + 12 = 19 = 12 + 7. This characteristic also applies to multiplication, but not subtraction or division. For instance, 8×5 Equals 40 and 5×8 = 40.

• Distributive Property: The multiplication of a whole number is distributed throughout the total or difference of the whole numbers, according to this property. It indicates that if two numbers say a and b, are multiplied by the same number c and then added, the total of a and b can be multiplied by c to yield the same answer. Like 2x(5+7)=2×5+2×7

Conclusion

Natural Numbers are positive integers that range from 1 to infinity. These are the numbers we normally count in our daily lives. Fractions, decimals, negative numbers, and zero are not considered natural numbers. The letter ‘N’ represents the set of Natural Numbers. Whole numbers are a collection of numbers that includes all-natural numbers as well as 0. They are real numbers that do not contain fractions, decimals, or negative values. Whole numbers are also considered as counting numbers. Natural numbers are numbers that range from one to infinity. Whole Numbers, on the other hand, begin at zero and go indefinitely. As a result, while every natural number is a Whole number, not every whole number is a natural number. Zero (0) is a whole number and not a natural number.