The first part of the course deals with the integers ℤ and the natural numbers ℕ. You know how to add and subtract, multiply and divide integers, and you know when one integer is bigger than another; we shall not review these things. One property of the integers which does need review is the principle of induction. It is the basis for most proofs involving natural numbers, for it gives a general procedure for verifying statements about all natural numbers (an infinite set). It comes in various formulations. Here is the first.