State whether Every whole number is a natural number or not

A number is defined as a mathematical value that is used to measure or count any value. A number is generally used for mathematical calculations. Numbers can be of types like whole number, natural number, integers, rational number, irrational number, real number  and complex numbers.

Number System

The number system is basically the representation of numbers using digits or symbols .it is a system that represents the numbers. it is used to define the set of values to be represented as quantity. The numbers used in the number system are used as digits typically ranging from 0 to 9. The number system is a mathematical notation for representing numbers using digits.

In the decimal number system, there are many types of numbers as mentioned earlier, like Integers, whole numbers, natural numbers, rational and irrational numbers, etc. They all are categorized based on their different characteristics. For instance, whole numbers are the integers that start from 0 and up to infinity, natural numbers generate from 1 and go up to infinity. Let’s look at the question given below,

State whether Every whole number is a natural number or not

In order to answer the above statement, it is important to first learn in detail what are whole numbers and what are natural numbers, lets start with understanding natural numbers,

Natural numbers

The other name for natural numbers is counting numbers as one can count the natural numbers with the use of hands. The natural numbers form a part of the number system which is positive integers from 1 onwards. These numbers are represented on the right side of a number line. The example of natural numbers are 1, 2, 3, 4, 5,… N. Zero and negative integers are not a part of natural numbers. The smallest natural number ever possible is 1 and the largest natural number can be any infinite positive integer value. Fractions, decimal values, complex numbers, etc, are not natural numbers. Examples of natural numbers are,

• 133 is a natural number as its a positive integer
• -78 is not a natural number as it’s not a positive integer
• 4.5 is not a natural number as it’s a decimal value.
• 7/53 is not a natural number as its a fraction

Whole numbers

Whole numbers are defined as numbers which include positive integers along with zero. similar to natural numbers, these numbers are represented on the right side of a number line. The smallest whole number possible is zero and the largest natural number can be any infinite positive integer value. A natural number is a subset of a whole number as all the natural numbers are whole numbers but all the whole numbers are not natural numbers exception being zero. fractions, decimal values, complex numbers, etc are not whole numbers. The example of whole numbers are 0, 1, 2, 3, 4, 5,…N. All the arithmetic operations can be performed on the whole numbers such as addition, subtraction, multiplications, etc. Examples of whole numbers are,

• 02 is a whole  number as its a positive integer
• -811 is not a whole  number as it’s not a positive integer
• 4.93 is not a whole number as it’s a decimal value.
• 2/89 is not a whole  number as its a fraction

Thus from the above definition of natural numbers and whole numbers, we can infer that natural number is a subset of whole number. The only difference between a whole number and a natural number is about the number zero which is present in a whole number only and not in a natural number. Therefore, every natural number is a whole number but every whole number is not a natural number.

Sample Problems

Question 1: Which of the following is a whole number – 1.2, 23, 09, 2/3, 4/4?

Answer:

• Taking first number that is 1.2, 1.2 is a decimal number and a decimal number cant be a whole number.
• Taking second number that is 23, 23 is a natural number as well as whole number.
• Taking third number that is 09, 09 is a natural number as well as whole number.
• Taking fourth number that is 2/3, 2/3 is a fraction thus it is not a whole number.
• Taking third number that is 4/4, solving this will give 1, which is both a whole and a natural number.

Question 2: Which of the following is a natural number –  2.3, 34, 03, 21/13?

Answer:

• Taking first number that is 2.3, 2.3 is a decimal number and a decimal number cannot be a natural number.
• Taking second number that is 34, 34 is a natural number as well as whole number.
• Taking third number that is 03, 03 is a natural number as well as whole number.
• Taking fourth number that is 21/13, 21/13 is a fraction thus it is not a natural number.