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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: