From: cate3.osbunorth@xerox.com (Henry Cate III) Subject: How to prove something ---------------------------------------------------- Survey of proof techniques This survey was written by Dana Angluin. Not really sure where it came from. Proof by example: The author gives only the case n=2 and suggests that it contains most of the ideas of the general proof. Proof by intimidation: 'Trivial.' Proof by vigorous handwaving: Works well in a classroom or seminar setting. Proof by cumbersome notation: Best done with access to at least four alphabets and special symbols. Proof by exhaustion: An issue or two of a journal devoted to your proof is useful. Proof by omission: 'The reader may easily supply the details.' 'The other 253 cases are analogous.' '...' Proof by obfuscation: A long plotless sequence of true and\or meaningless syntactically related statements. Proof by wishful citation: The author cites the negation, converse, or generalization of a theorem from the literature to support his claims. Proof by funding: How could three different government agencies be wrong? Proof by eminent authority: 'I saw Karp in the elevator and he said it was probably NP-complete.' Proof by personal communication: 'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal commmunication]. Proof by reduction to the wrong problem: 'To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.' Proof by reference to inaccessible literature: The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883. Proof by importance: A large body of useful consequences all follow from the proposition in question. Proof by accumulated evidence: Long and diligent search has not revealed a counterexample. Proof by cosmology: The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God. Proof by mutual reference: In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A. Proof by metaproof: A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques. Proof by picture: A more convincing form of proof by example. Combines well with proof by omission. Proof by vehement assertion: It is useful to have some kind of authority relation to the audience. Proof by ghost reference: Nothing even remotely resembling the cited theorem appears in the reference given. Proof by forward reference: Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first. Proof by semantic shift: Some standard but inconvenient definitions are changed for the statement of the result. Proof by appeal to intuition: Cloud-shaped drawings frequently help here. ---------------------------------------------------- Henry Cate III -------------- (ucbvax!xerox.com!cate3.osbunorth) OR (cate3.osbunorth@Xerox.Com) Everyone complains of his memory, no one of his judgment.