AP Calculus revisted (stolen from 1981 & 1982 Tep rush book) (or Everything You Always Wanted To Know About Calculus, but were afraid to pass) Part one: Proof techinques Proof by induction (used on equations with n in them. Induction techniques are very popular, even the Army uses them.) SAMPLE: Proof of induction without proof of induction. We know it's true for n equal to 1. Now assume that it's true for every natural number less than n. N is arbitrary, so we can take n as large as we want. If n is sufficiently large, the case of n+1 is trivially equivalent, so the only important n are n less than n. We can take n=n (from above), so it's true for n+1 becuase it's just about n. QED (QED translated from the Latin as "So what?") Proof by oddity SAMPLE: To prove that horses have an infinite number of legs. Horses have an even number of legs. They have two legs in back and fore legs in front. This makes a total of six legs, which certainly is an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore, horses must have an infinite number of legs. Topics is be covered in future issues include: Proof by intimidation gesticulation (handwaving) overwhelming evidence blatant assertion definition constipation (I was just sitting there and...) mutual consent changing all the 2's to n's lack of a counterexample elliptical reasoning bullet proof 86 proof it stands to reason try it; it works proof by linear combination of the abve .... and many, many more