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