1. Introduction to Whole Numbers
Whole numbers are one of the simplest and most commonly used types of numbers in math. If you understand natural numbers, whole numbers are just one small step ahead.
The easiest way to remember them is: Whole numbers are natural numbers plus zero.
This means whole numbers start from 0 and go on forever: 0, 1, 2, 3, 4, ...
2. Definition of Whole Numbers
Whole numbers are the set of non-negative numbers without fractions or decimals.
In mathematical notation:
\( \mathbb{W} = \{0, 1, 2, 3, 4, 5, ...\} \)
Whole numbers include:
- Zero
- All natural numbers
3. Why Are Whole Numbers Important?
Whole numbers are widely used in counting, measuring, and basic arithmetic. They help describe quantities that cannot be negative, like number of students, pages in a book, or days in a week.
4. Properties of Whole Numbers
Whole numbers follow several important mathematical properties that make calculations easy.
4.1. Closure Property
Whole numbers are closed under addition and multiplication.
- \( 4 + 7 = 11 \)
- \( 3 \times 5 = 15 \)
The results are always whole numbers.
4.2. Identity Property
Zero plays a special role in whole numbers.
4.2.1. Additive Identity
Adding 0 to any whole number keeps it the same.
\( a + 0 = a \)
4.2.2. Multiplicative Identity
Multiplying any whole number by 1 keeps it unchanged.
\( a \times 1 = a \)
4.3. No Negatives
Whole numbers do not include any negative numbers.
Examples:
- -1 is not a whole number
- -5 is not a whole number
4.4. Infinite Set
Whole numbers go on forever. There is no largest whole number.
5. Examples of Whole Numbers
- 0
- 5
- 10
- 99
- 1000
All of these are whole numbers because they are non-negative without decimals or fractions.
6. Whole Numbers in Real Life
Whole numbers appear everywhere in daily life because many real-world quantities cannot be negative.
6.1. Counting Objects
You can have 0 apples, 1 apple, or 10 apples — but never -3 apples.
6.2. Age
A person's age is always a whole number like 0, 1, 2, 20, or 50.
6.3. Money in a Wallet
You can have 0 rupees or more — but not negative rupees physically.
7. Difference Between Whole and Natural Numbers
Whole numbers and natural numbers are very similar, but there's one key difference.
7.1. Comparison Table
| Natural Numbers | Whole Numbers |
|---|---|
| Start at 1 | Start at 0 |
| No zero | Includes zero |
| \( \{1, 2, 3, ...\} \) | \( \{0, 1, 2, 3, ...\} \) |
8. Practice Questions
- Is 0 a whole number?
- Is 15 a whole number?
- Is -3 a whole number?
- Write the first six whole numbers.
- Does the set of whole numbers go on forever?
9. Summary
Whole numbers are the set of non-negative numbers starting from 0. They are used for counting and measuring things that cannot be negative. Whole numbers include 0 and all natural numbers.