Mathematical Induction

  This is a technique that is all too often overlooked in geometry. I include it here for completeness. Suppose P(n) is a sentence which is a statement for any , then the Principle of Mathematical Induction is

If we can prove the antecedent of this statement, , then by Modus ponens we can deduce . Thus there are two steps in the proof of :

Basic Step.

Prove P(1).

Inductive Step.

Prove .

Note that its name is misleading. Mathematical induction is deductive reasoning not inductive reasoning. Inductive reasoning is making a conjecture or guess based on observations and your previous mathematical experience.