# Are all natural numbers also whole numbers?

Answer

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Hint: We can conclude it by observing the definitions of both natural numbers and whole numbers and then consider a few examples in order to get clarity.

Complete step-by-step answer:

Let us look at the definitions of them:

NUMBER- A number tells us how many times a unit is contained in a given quantity.

Types of number system-

1) Binary number system

2) Octal number system

3) Hexadecimal number system

4) Roman number system

5) Decimal number system

DECIMAL NUMBER SYSTEM- Numeric values are represented by using digits from 0 to 9.

Again, numbers in the decimal system are classified as real numbers.

Real numbers are classified into rational numbers and irrational numbers.

Rational numbers are again classified into integer and non-integer rational numbers.

Again, integers are classified into-

1) Positive integer

2) Negative integer

3) Whole number

4) Natural number

NATURAL NUMBERS- Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.

N = {1, 2, 3, etc}

WHOLE NUMBERS- The system of Natural numbers along with number 0, is called whole number (W).

W = {0, 1, 2, 3, etc}

Hence, all natural numbers are also whole numbers.

Note: The vice versa does not hold that means all whole numbers are not natural numbers.

For suppose if you consider 0 it is a whole number but not a natural number.

Whereas, if you consider 1 it is both natural number and whole number.

Complete step-by-step answer:

Let us look at the definitions of them:

NUMBER- A number tells us how many times a unit is contained in a given quantity.

Types of number system-

1) Binary number system

2) Octal number system

3) Hexadecimal number system

4) Roman number system

5) Decimal number system

DECIMAL NUMBER SYSTEM- Numeric values are represented by using digits from 0 to 9.

Again, numbers in the decimal system are classified as real numbers.

Real numbers are classified into rational numbers and irrational numbers.

Rational numbers are again classified into integer and non-integer rational numbers.

Again, integers are classified into-

1) Positive integer

2) Negative integer

3) Whole number

4) Natural number

NATURAL NUMBERS- Numbers starting from 1, having no fraction part, which we use in counting the objects, denoted by N.

N = {1, 2, 3, etc}

WHOLE NUMBERS- The system of Natural numbers along with number 0, is called whole number (W).

W = {0, 1, 2, 3, etc}

Hence, all natural numbers are also whole numbers.

Note: The vice versa does not hold that means all whole numbers are not natural numbers.

For suppose if you consider 0 it is a whole number but not a natural number.

Whereas, if you consider 1 it is both natural number and whole number.

Last updated date: 18th Sep 2023

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