Short Answer
Whole numbers are the set of numbers that include zero along with all natural numbers. They start from 0 and continue endlessly like 0, 1, 2, 3, 4, and so on. These numbers are used for counting as well as representing the absence of quantity.
The main difference between whole numbers and natural numbers is that natural numbers start from 1, while whole numbers start from 0. So, zero is included in whole numbers but not in natural numbers.
Detailed Explanation:
Whole numbers
Whole numbers are a group of numbers that include all natural numbers along with zero. These numbers are used in basic counting as well as to represent situations where there is nothing or no quantity. Whole numbers start from 0 and increase endlessly. They are always non-negative, meaning they are never less than zero. The set of whole numbers is written as:
W = {0, 1, 2, 3, 4, 5, …}
- Definition of whole numbers
Whole numbers are defined as all the counting numbers together with zero. They include numbers like 0, 1, 2, 3, and so on. These numbers are simple and easy to use in daily life. Zero plays an important role here because it represents nothing or no quantity.
- Examples of whole numbers
Examples of whole numbers are 0, 1, 2, 3, 4, 5, and so on. For instance, if there are no books on a table, we use 0 to represent that situation. If there are 6 apples, then 6 is also a whole number.
- Properties of whole numbers
Whole numbers follow basic mathematical rules. When we add or multiply two whole numbers, the result is always a whole number. For example, 2 + 3 = 5 and 4 × 2 = 8. However, subtraction may not always give a whole number, such as 3 − 5, which gives a negative number. Whole numbers also include zero, which is the smallest whole number.
- Use in daily life
Whole numbers are used in many daily situations. We use them to count objects, measure quantities, and show zero quantity. For example, counting students in a class, number of items in a shop, or showing no balance in an account.
Difference from natural numbers
Whole numbers and natural numbers are very similar, but they have one important difference. Natural numbers start from 1 and include numbers like 1, 2, 3, and so on. They are mainly used for counting objects. On the other hand, whole numbers include all natural numbers plus zero.
- Starting point
Natural numbers start from 1, while whole numbers start from 0. This means zero is included only in whole numbers.
- Inclusion of zero
Zero is not a natural number, but it is a whole number. This is the main difference between the two sets.
- Representation
Natural numbers are written as N = {1, 2, 3, …}
Whole numbers are written as W = {0, 1, 2, 3, …}
- Practical meaning
Natural numbers are used when counting objects like 1 apple, 2 books, etc. Whole numbers are used when we also need to show zero quantity, like 0 apples or no items.
Conclusion
Whole numbers include zero and all natural numbers, while natural numbers start from 1 only. The inclusion of zero makes whole numbers different and more useful in situations where we need to represent nothing or no quantity.