52 lines
1.5 KiB
Plaintext
52 lines
1.5 KiB
Plaintext
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
|
|
|