*Weak Mathematical Induction:*If the following two things can be shown about a proposition :**Base Case:**is true.**Induction Step:**If is true, then is true.

*Strong Mathematical Induction:*If the following two things can be shown about a proposition :**Base Case:**is true.**Induction Step:**If is true , , then is true.

*Pigeonhole Principle:*If there are pigeons and they are put in pigeonholes, then there is a pigeonhole that contains at least two pigeons.*Well Ordering Principle (WOP):*If is a non-empty set that is a subset of the positive integers, then has a least element.*Transitivity:*If and , then .*Substitution:*If , then can be substituted for in any statement without changing the veracity(truthfulness) of the statement.*Distributive Property:*.

Gregory Stoll 2000-04-08