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Old 2010-04-06, 08:34   #1
10metreh's Avatar
Nov 2008

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Default 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.

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."
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Old 2010-04-06, 16:54   #2
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Originally Posted by 10metreh View Post
But I thought most members would like this.
I like...
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