📌 Classification of Numbers in Mathematics

Numbers are classified into different types based on their properties. Below is a structured breakdown:

🔢 1. Natural Numbers (N) & Whole Numbers (W)

✔ Natural Numbers (N): Counting numbers starting from 1.
📌 Examples: 1, 2, 3, 4, 5, …

✔ Whole Numbers (W): Natural numbers + 0.
📌 Examples: 0, 1, 2, 3, 4, …

🔢 2. Integers (Z)

✔ Integers (Z): Whole numbers and their negatives.
📌 Examples: … -3, -2, -1, 0, 1, 2, 3, …

💡 Fact: Every whole number is an integer, but not every integer is a whole number.

🔢 3. Rational Numbers (Q)

✔ Rational Numbers (Q): Numbers that can be written as a fraction (p/q), where:

• p and q are integers
• q ≠ 0

📌 Examples:

• 1/2
• 3/4
• 0.3333… = 1/3 (Repeating Decimal)
• 0.25 = 1/4 (Terminating Decimal)

🔢 4. Irrational Numbers

✔ Irrational Numbers: Cannot be written as fractions and have non-terminating, non-repeating decimals.

📌 Examples:

• π = 3.1415926535… (never repeats)
• √2 = 1.41421356…

🔢 5. Real Numbers (R)

✔ Real Numbers (R): All Rational and Irrational Numbers combined.
✔ Represented on a number line.
✔ Includes: Integers, fractions, terminating & repeating decimals, surds.

💡 Fun Fact: Every number you’ve ever used in daily life is a Real Number!

🔢 6. Prime & Composite Numbers

✔ Prime Numbers: Divisible only by 1 and itself.
📌 Examples: 2, 3, 5, 7, 11, 13, 17, 19…

✔ Composite Numbers: Have more than two factors.
📌 Examples: 4 (1,2,4), 6 (1,2,3,6), 8 (1,2,4,8)

🔢 7. Even & Odd Numbers

✔ Even Numbers: Divisible by 2.
📌 Examples: 2, 4, 6, 8, 10…

✔ Odd Numbers: Not divisible by 2.
📌 Examples: 1, 3, 5, 7, 9…

🔢 8. Complex Numbers (C)

✔ Complex Numbers: Extend real numbers by including imaginary numbers (i), where i² = -1.

📌 General form: (a + bi), where a, b are real numbers.

📌 Examples:

• 2 + 3i
• -5 + 4i