Number Systems

Numbers are classified into

Numbers are classified into: Natural numbers (N) = {1, 2, 3, ...}, Whole numbers (W) = {0, 1, 2, 3, ...}, Integers (Z) = {..., -2, -1, 0, 1, 2, ...},

A rational number can be written

A rational number can be written as p/q where p and q are integers and q ≠ 0. Examples: 3/4, -7/5, 25 (= 25/1). Key property: decimal expansion is eit

Numbers that cannot be expressed as

Numbers that cannot be expressed as p/q where p, q are integers and q ≠ 0. Examples: √2, √3, π, 0.10110111011110... Key property: decimal expansion is

Three types

Three types: Terminating (ends after finite digits, like 0.75), Non-terminating recurring (repeats a pattern, like 0.333... or 1.272727...), Non-termi

Key rules

Key rules: Rational + Rational = Rational, Irrational + Irrational = may be rational or irrational (√2 + √2 = 2√2 is irrational, but √2 + (-√2) = 0 is