Proof and Mathematical Induction (HL)

A mathematical proof is a watertight logical argument establishing that a statement is true for every case it claims to cover. Checking a formula for a few values may build confidence, but it is not proof — a single counterexample can destroy a pattern that held for a thousand cases. At Higher Level you meet several styles of rigorous argument, of which the most important for this unit is proof by mathematical induction.

Induction proves statements of the form "$P(n)$ is true for all integers $n \geq n_0$," where $n_0$ is a starting value (usually 1). The method rests on a domino intuition: if the first domino falls, and each fallen domino knocks over the next, then every domino falls. Formally, a proof by induction has three parts. (1) Base case: show that $P(n_0)$ is true, typically by d