.Open Proofs For an introduction see .See ./logic_20_Proofs100.html which give informal hints and discusses some philophical ideas associated with proofs and some tools and automation, or .See ./logic_25_Proofs.html which presents an attempt at a practical yet formal way of presenting proofs in a machine readable, renderable, and checkable form. . Tools for Proofs (ProofBuilder): hamburger helper for budding logicians .See http://www.cis.gvsu.edu/~mcguire/ProofBuilder/pub/2007_sigcse/poster.html .Open Proofs that are not proofs .Source .See [RentelnDundes05] (JANUARY 2005 NOTICES OF THE AMS 29) .Net . Proof by vigorous handwaving Works well in a classroom or seminar setting. . 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 funding How could three different government agencies be wrong? . 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 omission "The reader may easily supply the details." "The other 253 cases are analogous." . Proof by deferral "We'll prove this later in the course." . Proof by picture A more convincing form of proof by example. Combines well with proof by omission. . Proof by intimidation "Trivial." . Proof by seduction "Convince yourself that this is true!" . 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 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 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 NPcomplete [Karp, personal communication]." . 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 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 semantic shift Some of the standard but inconvenient definitions are changed for the statement of the result. . Proof by appeal to intuition Cloud-shaped drawings frequently help here. . What is the difference between an argument and a proof? An argument will convince a reasonable man, but a proof is needed to convince an unreasonable one. .Close.Net .Close .Close Proofs