REAL NUMBERS
Completion requirements
Natural Numbers (ℕ): {1, 2, 3, 4, …}
Used for counting.
Closed under addition and multiplication.
Integers (ℤ): {…, -3, -2, -1, 0, 1, 2, 3, …}
Extends natural numbers by including zero and negative numbers.
Allows subtraction.
Rational Numbers (ℚ): {a/b | a, b are integers, b ≠ 0}
Includes fractions and whole numbers.
Allows division (except by zero).
Irrational Numbers: {√2, π, e, …}
Cannot be written as a fraction (a/b form).
Decimal representation is non-repeating and non-terminating.
Real Numbers (ℝ):
Includes both rational and irrational numbers.
Represents all points on a number line.