Number Systems and Properties
Types of numbers: - Natural numbers: 1, 2, 3, ... (counting numbers) - Whole numbers: 0, 1, 2, 3, ... - Integers: ..., −2, −1, 0, 1, 2, ... (positive and negative whole numbers) - Rational numbers: expressible as p/q (includes integers, fractions, terminating and repeating decimals) - Irrational numbers: cannot be expressed as a fraction (π, √2, √3) - Real numbers: all rational and irrational numbers combined
Properties: - Commutative: a + b = b + a; a × b = b × a - Associative: (a + b) + c = a + (b + c) - Distributive: a(b + c) = ab + ac
Order of operations (PEMDAS): Parentheses → Exponents → Multiplication/Division (left to right) → Addition/Subtraction (left to right)
Absolute value |x|: Distance from zero. Always ≥ 0. |−7| = 7.