a. Natural Numbers (ℕ)

• Definition: Counting numbers starting from 1.

• Examples: 1, 2, 3, 4, 5, ...

• Note: 0 is not a natural number.

b. Whole Numbers

• Definition: Natural numbers including 0.

• Examples: 0, 1, 2, 3, 4, ...

c. Integers (ℤ)

• Definition: Whole numbers and their negative counterparts.

• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...

d. Rational Numbers (ℚ)

• Definition: Numbers that can be expressed as a fraction (p/q), where q ≠ 0.

• Examples: 1/2, -3/4, 5, 0 (since 5 = 5/1, 0 = 0/1)

• Terminating and Repeating decimals are rational.

e. Irrational Numbers

• Definition: Numbers not expressible as a fraction. Their decimal expansion is non-terminating and non-repeating.

• Examples: √2, π, e

f. Real Numbers (ℝ)

• Definition: All rational and irrational numbers.

• Includes: Natural, whole, integers, rational, and irrational.

g. Imaginary and Complex Numbers

• Imaginary: Involves √(-1), denoted as i or j.

• Complex: Numbers in the form a + bi, where a and b are real.