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2010-04-06, 08:34   #1
10metreh

Nov 2008

2·33·43 Posts
Proof techniques

After getting insulted by Random Poster for rambling on in a proof, I decided to post this list of proof techniques. Some of you may have seen this before; Bob will accuse me of violating a copyright. But I thought most members would like this.

Quote:
 Proof Techniques Proof by Contradiction: "This theorem contradicts a well-known result due to Isaac Newton." Proof by Metacontradiction: "We prove that a proof exists. To do so, assume that there is no proof..." Proof by Deferral: "We'll prove this next week." Proof by Cyclic Deferral: "As we proved last week..." Proof by Indefinite Deferral: "As I said last week, we'll prove this next week." Proof by Intimidation: "As any fool can see, the proof is obviously trivial." Proof by Deferred Intimidation: "As any fool can see, the proof is obviously trivial." "Sorry, Professor, are you sure?" Goes away for half an hour. Comes back. "Yes." Proof by Handwaving: "Self-explanatory." Most effective in seminars and conference talks. Proof by Vigorous Handwaving: More tiring, but more effective. Proof by Over-optimistic Citation: "As Pythagoras proved, two cubes never add up to a cube." Proof by Personal Conviction: "It is my profound belief that the quaternionic pseudo-Mandelbrot set is locally disconnected." Proof by Lack of Imagination: "I can't think of any reason why it's false, so it must be true." Proof by Forward Reference: "My proof that the quaternionic pseudo-Mandelbrot set is locally disconnected will appear in a forthcoming paper." Often not as forthcoming as it seemed when the reference was made. Proof by Example: "We prove the case n = 2 and then let 2 = n." Proof by Omission: "The other 142 cases are analogous." Proof by Outsourcing: "Details are left to the reader." Statement by Outsourcing: "Formulation of the correct theorem is left to the reader." Proof by Unreadable Notation: "If you work through the next 500 pages of incredibly dense formulas in six alphabets, you'll see why it has to be true." Proof by Authority: "I saw Milnor in the cafeteria and he said he thought it's probably locally disconnected." Proof by Personal Communication: "The quaternionic pseudo-Mandelbrot set is locally disconnected (Milnor, personal communication)." Proof by Vague Authority: "The quaternionic pseudo-Mandelbrot set is well-known to be locally disconnected." Proof by Provocative Wager: "If the quaternionic pseudo-Mandelbrot set is not locally disconnected, I'll jump off London Bridge wearing a gorilla suit." Proof by Erudite Allusion: "Local connectivity of the quaternionic pseudo-Mandelbrot set follows by adapting the methods of Cheesburger and Fries to non-compact infinite-dimensional quasi-manifolds over skew fields of characteristic greater than 11." Proof by Reduction to the Wrong Problem: "To see that the quaternionic pseudo-Mandelbrot set is locally disconnected, we reduce it to Pythagoras's Theorem." Proof by Inaccessible Reference: "A proof that the quaternionic pseudo-Mandelbrot set is locally disconnected can be easily derived from Pzkrzwcziewszczii's privately printed memoir bound into volume 1 1/2 of the printer's proofs of the 1831 Proceedings of the South Liechtenstein Ladies' Knitting Circle before the entire print run was pulped."

2010-04-06, 16:54   #2
petrw1
1976 Toyota Corona years forever!

"Wayne"
Nov 2006

138316 Posts

Quote:
 Originally Posted by 10metreh But I thought most members would like this.
I like...

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