Difference Between Natural and Whole Numbers

Natural numbers are the numbers we use for counting things in our daily life, like counting apples, pencils, or people. They start from 1 and keep increasing by 1 each time — 1, 2, 3, 4, and so on, continuing without any end. Because they are used for counting, natural numbers are also called counting numbers.

We can show the set of natural numbers as: 
N = {1,2,3,4,5,… }

So, every natural number helps us count objects, and there is always another number after it, therefore natural numbers never stop!

Whole numbers are numbers that start at 0 and continue as 1, 2, 3, 4, and so on, continuing without end. Whole numbers include all counting numbers, and also 0. The whole number 0 shows that there is no quantity (nothing). Whole numbers do not include fractions, decimals, or negative numbers.

We use the following symbol to represent the set of whole numbers: 
W = {0,1,2,3,4,5,…}
 

So, whole numbers are just like natural numbers, except whole numbers start with “0.”

In mathematics, natural and whole numbers are fundamental concepts. Natural and whole numbers have similarities, but they also differ in some ways. In this section, we will learn the difference between natural and whole numbers. 

Natural numbers refer to the numbers that naturally count up from 1 in the positive direction (1, 2, 3..., etc.), and whole numbers include the number zero as the first whole number (0, 1, 2, 3..., etc.). Here are a few strategies to help students distinguish between the two and thoroughly comprehend these concepts:
 

• Be sure to emphasize at some point that zero is part of whole numbers and is not part of natural numbers. It is important that students understand zero is the identity element for the operation of addition!
   
• Use a number-line representation set up for natural numbers and whole numbers. The natural number on number line starts at 1 and the whole number on number line starts symmetrically at zero. A gap exists at parent zero for natural numbers.
   
• Leverage real-world contexts by using natural numbers when counting physical items and whole numbers when tracking inventory levels that may be zero.
   
• Set notation exercises can be effective; writing out set N = {1, 2, 3, ...} versus set W= {0, 1, 2, 3, ...} forces students to explain the notation in symbols.
   
• Practice with true-false statements; for example, "Zero is a natural number." Challenge yourself to justify their answer for depth of reasoning about the concepts. 

Natural and whole numbers are an essential part of representing quantities, locations, and measurements in real-life situations.
 

• Sports: In sports, the ranking of a tournament is represented by natural numbers with the 1st place being represented as 1, 2nd place represented as 2, etc. In games, scoring will often start at 0, which is a whole number.
   
• Computer Programming: In computer science, arrays and lists made use of zero-indexing, therefore, whole numbers are common in this situation.
   
• Phone Numbers: A whole number is also used in the country code and area code of a phone number, which will often start with a 0.
   
• Floors in a Building: When differentiating floors in a building, we will sometimes see 0 associated with the ground floor and a natural number will be assigned to each subsequent floor.
   
• Digital Clocks: When telling time using a digital format, it will start at 0 hours, 0 minutes, and 0 seconds at 00:00, which is a whole number, and will continue to count throughout the day using whole numbers.