Number System Explained
1. Natural Numbers
These are the counting numbers: 1, 2, 3, 4, 5, ...
Example: 1, 2, 3, 4, 5…
2. Whole Numbers
Natural numbers plus 0.
Example: 0, 1, 2, 3, 4, 5…
3. Integers
Whole numbers and their negative versions.
Example: …-3, -2, -1, 0, 1, 2, 3…
4. Rational Numbers
Numbers that can be written as a fraction (p/q), where p and q are integers and q ≠ 0.
Example: 4 (can be written as 4/1), ¾, -2/5.
5. Irrational Numbers
Numbers that cannot be written as fractions. They are non-repeating and non-terminating decimals.
Example: √2, √3, π, e.
6. Real Numbers
All numbers: natural, whole, integers, rational, and irrational numbers.
Example: 5, -3, 0.75, √2, π.
7. Even Numbers
Numbers divisible by 2.
Example: 2, 4, 6, 8…
8. Odd Numbers
Numbers not divisible by 2.
Example: 3, 5, 7, 9…
9. Prime Numbers
Numbers with only two factors: 1 and itself.
Example: 2, 3, 5, 7…
10. Twin Primes
Two prime numbers with a difference of 2.
Example: (3, 5), (5, 7), (11, 13)…
11. Co-prime Numbers
Two numbers with a GCD of 1.
Example: (3, 4), (13, 15).
12. Composite Numbers
Numbers with more than two factors (not prime).
Example: 4, 6, 9, 16…
Note: 1 is neither prime nor composite.
13. Perfect Numbers
Numbers where the sum of their factors (excluding itself) equals the number.
Example: 6 (1 + 2 + 3 = 6), 28, 496.
14. Complex Numbers
Numbers with a real part and an imaginary part (i = √-1).
Example: 3 + 4i, 5 + 6i.
15. Face Value
The actual value of a digit in a number.
Example: In 6728, the face value of 6 is 6, and 7 is 7.
16. Place Value
The value of a digit based on its position in the number.
Example: In 6729:
- Place value of 9 = 9 × 1 = 9
- Place value of 2 = 2 × 10 = 20
- Place value of 7 = 7 × 100 = 700