JCHL Number Theory 1: Types of Numbers

Learning work

• Natural numbers (N) = whole positive numbers 1, 2, 3, …
• Prime = a natural number with exactly two divisors (1 and itself); 1 is NOT prime
• Composite = a natural number with MORE than two divisors; integers (Z) = all whole numbers, positive, negative and 0
• Rational (Q) = can be written, in its simplest form, as a fraction a/b where a and b are integers and b ≠ 0 — this includes all integers and all terminating and recurring decimals (0.3̇ = ⅓)
• Irrational = a number that CANNOT be written, in its simplest form, as such a fraction a/b (e.g. √3, π); its decimal never stops and never repeats
• Real (R) = all the rational and irrational numbers together — every number on the number line
• The big thing to learn is the SYMBOLS — a question says "x ∈ N" rather than "natural number"