Natural numbers are a set of positive integers that start from 1 and continue indefinitely. They are also known as counting numbers.
Characteristics of natural numbers:
1. Positive integers only (no zero, negatives, or fractions)
2. Start from 1 (1, 2, 3, 4, 5, …)
3. Infinite (never-ending)
4. Can be added, subtracted, multiplied, and divided (except division by zero)
Examples of natural numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
Key properties:
1. Closure: The sum, product, and difference of two natural numbers is always a natural number.
2. Commutativity: The order of addition or multiplication doesn’t change the result.
3. Associativity: The order of operations doesn’t change the result.
Real-life applications:
1. Counting objects
2. Measuring time (days, hours, minutes)
3. Measuring length (inches, feet, yards)
4. Basic arithmetic operations
Note the difference between natural numbers and whole numbers:
Natural numbers: 1, 2, 3, 4, 5, …
Whole numbers: 0, 1, 2, 3, 4, 5, …
Natural numbers exclude zero, while whole numbers include zero.
