1. Introduction to Natural Numbers
Natural numbers are the numbers we use for basic counting in everyday life. When you count objects like 1 apple, 2 apples, or 3 apples, you are using natural numbers.
They are the simplest form of numbers and are usually the first numbers students learn.
Natural numbers begin from 1 and go on endlessly: 1, 2, 3, 4, ...
2. Definition of Natural Numbers
Natural numbers are defined as the set of positive counting numbers. They do not include decimals, fractions, or negative numbers.
In mathematical notation, natural numbers are written as:
\( \mathbb{N} = \{1, 2, 3, 4, 5, ...\} \)
3. Why Are They Called 'Natural'?
They are called natural because they naturally arise when humans start counting things around them. Even without learning math formally, children begin counting using natural numbers.
4. Properties of Natural Numbers
Natural numbers follow some basic mathematical properties that make them easy to work with.
4.1. Closure Property
If you add or multiply two natural numbers, the result is always a natural number.
Examples:
- \(2 + 3 = 5\)
- \(4 \times 5 = 20\)
4.2. No Zero or Negative Numbers
Natural numbers do not include 0 or any negative number.
Examples:
- 0 is not a natural number
- -3 is not a natural number
4.3. Infinite Set
You can keep counting natural numbers forever. There is no largest natural number.
Example: After 100 comes 101, then 102, and so on...
5. Examples of Natural Numbers
- Counting objects: 1 book, 2 books, 3 books
- Counting people: 1 person, 2 people...
- Steps you walk: 1 step, 2 steps...
6. Difference Between Natural and Whole Numbers
Many students confuse natural numbers with whole numbers. Here is the difference:
6.1. Comparison Table
| Natural Numbers | Whole Numbers |
|---|---|
| Start from 1 | Start from 0 |
| No zero | Includes 0 |
| \( \{1, 2, 3, ...\} \) | \( \{0, 1, 2, 3, ...\} \) |