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Topic: Proof by exhaustion

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	NationMaster - Encyclopedia: Proof by exhaustion
		Proof by exhaustion, also known as the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases, and each case is proved separately.
		The first proof of the four colour theorem was a proof by exhaustion with 1,936 cases.
		Proof by verbosity should not be confused with proof by exhaustion, the latter being a valid form of proof.
	www.nationmaster.com /encyclopedia/Proof-by-exhaustion (1014 words)

	Proof by exhaustion - Wikipedia, the free encyclopedia
		Proof by exhaustion, also known as the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases, and each case is proved separately.
		A proof that the cases are exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases.
		The first proof of the four colour theorem was a proof by exhaustion with 1,936 cases.
	en.wikipedia.org /wiki/Proof_by_exhaustion (462 words)

	Proof by verbosity - Wikipedia, the free encyclopedia
		Proof by verbosity is a term used to describe an excessively verbose mathematical proof that may or may not actually prove the result.
		Proof by verbosity should not be confused with proof by exhaustion, the latter being a valid form of proof.
		The difference lies in that a proof by exhaustion is used when a number of dissimilar cases must be independently proven, whereas a proof by verbosity tends to be repetitive, with many overlapping proofs for specific cases of a more general problem.
	en.wikipedia.org /wiki/Proof_by_verbosity (196 words)

	proof by exhaustion - Information from Reference.com
		In Proof by exhaustion, the conclusion is established by dividing it into a finite
		Proof by Exhaustion: This is a modification of an inductive proof.
		vigorous handwaving; 1.4 Proof by cumbersome notation; 1.5 Proof by exhaustion...
	www.reference.com /search?q=proof%20by%20exhaustion&db=web (228 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		Proof by exhaustion: An issue or two of a journal devoted to your proof is sufficient.
		Proof by cosmology: The negation of the proposition is unimaginable or meaningless.
		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.
	www.cs.rice.edu /~ian/Public/Humor/proofs (362 words)

	Mathematical proof (Site not responding. Last check: 2007-10-27)
		In the context of proof theory where purely formal proofs are considered not entirely formal demonstrations in mathematics are called "social proofs".
		philosophy of mathematics is concerned with the role of and logic in proofs and mathematics as a language.
		Proof by contradiction (also known as reductio ad absurdum): where it is shown that if property were true a logical contradiction occurs the property must be false.
	www.freeglossary.com /Mathematical_proof (906 words)

	Prove It! (Site not responding. Last check: 2007-10-27)
		Proof by exhaustion: ------------------- An issue or two of a journal devoted to your proof is useful.
		Proof by cosmology: ------------------ The negation of the proposition is unimaginable or meaningless.
		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.
	www.slonet.org /~tellswor/prove-it.htm (376 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		Proof by exhaustion: An issue or two of a journal devoted to your proof is useful.
		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.
	www.textfiles.com /humor/proof.met (472 words)

	PlanetMath: techniques in mathematical proofs
		The following example (from ring theory) illustrates the one aspect of proofs in mathematics: proving the existence of certain mathematical objects or properties.
		Proof by mathematical induction, proof by contradiction, proof by exhaustion, and proof by similarity are just some of the major techniques.
		This is version 4 of techniques in mathematical proofs, born on 2004-10-24, modified 2006-03-20.
	planetmath.org /encyclopedia/ConstructiveProof.html (193 words)

	Humor Maze (proof) (Site not responding. Last check: 2007-10-27)
		Proof by reduction to the wrong problem: 'To see that infinite- dimensional colored cycle stripping is decidable, we reduce it to the halting problem.' 12.
		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 mutual reference: In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown 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.
	www.pair-of-dice.com /luke/maze/proof.html (503 words)

	Proof by exhaustion (Site not responding. Last check: 2007-10-27)
		Proof by exhaustion, also known as the brute force method or case analysis,is a method of mathematical proof in which the statement to beproved is split into a finite number of cases, and each case is proved separately.
		This proof was controversial because the majority of the cases were checked by acomputer program, not by hand.
		Mathematicians prefer to avoid proofs with large numbers of cases because these proofs feel inelegant - they leave animpression that the theorem is only true by coincidence, and not because of some underlying principle or connection.
	www.therfcc.org /proof-by-exhaustion-75807.html (422 words)

	[No title]
		An issue or two of a journal devoted to your proof is useful.
		Popular for proofs of the existence of God.
		A method is given to construct the desired proof.
	www.cs.uiuc.edu /class/fa06/cs273/Links/how-to-prove-it.html (352 words)

	Proof by exhaustion: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-27)
		The method of exhaustion is a way of finding the area or volume of a shape that is not easily defined in terms of traditional shapes....
		Mathematicians prefer to avoid proofs with large numbers of cases because these proofs feel inelegant—they leave an impression that the theorem is only true by coincidence, EHandler: no quick summary.
		(a proof by infinite descent is a particular kind of proof by mathematical induction....
	www.absoluteastronomy.com /encyclopedia/p/pr/proof_by_exhaustion.htm (1104 words)

	[No title] (Site not responding. Last check: 2007-10-27)
		Proof (by intimidation): First, it is necessary to prove that all horses have the same number of legs.
		Proof by Misconception: An example of this is the Freshman's Conception of the Limit Process: "2 equals 3 for large values of 2." Once introduced, any conclusion is reachable.
		Proof by Exhaustion: This is a modification of an inductive proof.
	www.math.niu.edu /~rusin/papers/teaching-math/dumbproofs (1167 words)

	Making Mathematics: Mathematics Research Teacher Handbook
		Proof exercises not connected to the study of a particular content area (e.g., triangle congruence or induction) force students to think about which of their many skills might help solve the problem.
		The proof had that "mathy" look to it, but, until the student had a better grasp of the underlying structures of the problem and their properties, she was in no position to develop a useful system of symbols.
		Proof: Since we have at least one clean thrower, there are more pies remaining than throwers and by the pigeonhole principle, at least one thrower must be hit by more than one pie.
	www2.edc.org /makingmath/handbook/Teacher/Proof/Proof.asp (15210 words)

	Illustration of proper mathematics proof and solution
		It is the method of proof by exhaustion of all the cases.
		The proof of the second assertion rests on the observation that a convex n-gon can be partitioned into n-2 triangles and that the sum of the angles from all these triangles equals the sum of the internal angles of the polygon.
		Aside from being motivators of proof design, illustrations serve two uses: (a) in clarifying an argument in a proof and (b) in showing that a statement is false.
	www.mathpath.org /MathPath_Quiz_2003_files/example.htm (2260 words)

	CS655: Manifest 5 April 2001 (Site not responding. Last check: 2007-10-27)
		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 Icelandic Philological Society, 1883.
		Proof by vehement assertion: It is useful to have some kind of authority relation to the audience, so this is particularly useful in classroom settings.
		Proof by lack of space: "The proof is not detailled due to lack of space in this proceedings..." works well in conjunction with proof by forward reference.
	www.cs.virginia.edu /~evans/cs655/manifests/0405.html (350 words)

	Proof Techniques (Site not responding. Last check: 2007-10-27)
		This is a list of proof techniques which are very powerful, but unfortunately not valid.
		An issue or two of a journal devoted to your proof is useful.
		A method is given to construct the desired proof.
	www.cse.ucsc.edu /~martine/light/proofs.html (321 words)

	Proof
		These proofs will be more efficient that the proofs by Exhaustion that we used in Discovery, Number, Level 6.
		You will see that this algebraic proof is much more efficient than the Proof by Exhaustion in that it once we have it, it takes many fewer lines to write out.
		Proof of Conjecture 11: The method that we will use here is more difficult than the one we have already used for 2-, 3- and 4-digit numbers.
	www.nzmaths.co.nz /Algebra/Units/proof.aspx (5731 words)

	How to prove it [rec.humor.funny]
		proof by obfuscation: A long plotless sequence of true and/or meaningless syntactically related statements.
		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 semantic shift: Some of the standard but inconvenient definitions are changed for the statement of the result.
	www.netfunny.com /rhf/jokes/88q4/nonbook/proof.119.html (440 words)

	Proof by contradiction - Hutchinson encyclopedia article about Proof by contradiction
		Method of proof in which it is initially assumed that the proposition which it is desired to prove is not true.
		If it can then be shown that this assumption leads logically to a contradiction or ‘absurdity’, it will have been proved that the original proposition must be true.
		This information should not be considered complete, up to date, and is not intended to be used in place of a visit, consultation, or advice of a legal, medical, or any other professional.
	encyclopedia.farlex.com /Proof+by+contradiction (112 words)

	Proof By Exhaustion (Site not responding. Last check: 2007-10-27)
		There is no proof yet that this happens in human beings but exercise during...
		Abstract painter Tomma Abts was cited by the judges as proof that painting is...
		Sometimes there may be a few dozen - for example, rigorously solving an end-game puzzle in chess might involve considering a dozen or more possible lines of moves.
	www.wikiverse.org /proof-by-exhaustion (582 words)

	Definition of Proof by exhaustion
		Proof by exhaustion, also known as the brute force method or case analysis, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases, and each case is proved separately.
		To prove that every cube number is either a multiple of 9 or is 1 more or 1 less than a multiple of 9.
		For example, rigorously solving an end-game puzzle in chess might involve considering a dozen or more possible lines of moves.
	www.wordiq.com /definition/Proof_by_exhaustion (480 words)

	Supreme Court Preview: October 2006 Merit Briefs (ABA Division for Public Education)
		Whether the PLRA prescribes a "total exhaustion" rule that requires a federal district court to dismiss a prisoner's federal civil rights complaint for failure to exhaust administrative remedies whenever there is a single unexhausted claim, despite the presence of other exhausted claims.
		Consolidated with 05-7142 and one hour allotted for oral argument.
		Whether the PLRA requires a prisoner to name a particular defendant in his or her administrative grievance in order to exhaust his or her administrative remedies as to that defendant and to preserve his or her right to sue them.
	www.abanet.org /publiced/preview/briefs/oct06.shtml (946 words)

	Invalid techniques of proof (Site not responding. Last check: 2007-10-27)
		In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A. 1.18 Proof by metaproof
		We were asked in an exercise to proof this theorem.
		This method of proof is one of the two pillars of modern cryptography.
	www.maths.uwa.edu.au /~berwin/humour/invalid.proofs.html (848 words)

	Talk:Proof by exhaustion - InformationBlast
		I don't think that proof by exhaustion itself is controversial at all among mathematicians -- but its application or use in particular circumstances (e.g.
		The logical validity of proof by exhaustion is not in doubt, but its application and veracity in concrete cases by mortal humans is another matter.
		Specific applications of this method of proof may be controversial, but the method itself is not.
	www.informationblast.com /Talk:Proof_by_exhaustion.html (165 words)

	JYI Resources: Proof Techniques (Site not responding. Last check: 2007-10-27)
		This is a more refined form of proof by obfuscation.
		This is a modification of an inductive proof.
		Instead of going to the general case after proving the first one, prove the second case, then the third, then the fourth, and so on - until a sufficiently large n is achieved whereby the nth case is being propounded to a soundly sleeping audience.
	www.jyi.org /resources/humor/proofs.html (258 words)

	Anime Scores Forum :: View topic - Invalid Proof Techniques (Site not responding. Last check: 2007-10-27)
		Proof by cumbersome notation in itself is not invalid...unless within the cumbersome notation, another fallacy is involved...most logic classes are taught using "cumbersome notation" to teach logic rules and to distinguish between spoken intent in a statement and the logic it represents...
		Anyways...I'm curious as to what proof the author of this list has to show that these are all invalid...or if this is all suppose to just be accepted by (proof by) appeal to intuition...lol...
		Anyways...I'm curious as to what proof the author of this list has to show that these are all invalid...
	www.animescores.com /forum/viewtopic.php?t=5118 (940 words)

	Debating 101 - Logic Fallacies (Site not responding. Last check: 2007-10-27)
		PROOF: Identify the threat and the proposition and argue that the threat is unrelated to the truth or falsity of the proposition.
		PROOF: Show that the correlation is coincidental by showing that: (i) the effect would have occurred even if the cause did not occur, or (ii) that the effect was caused by something other than the suggested cause.
		PROOF: Identify the word which is used twice, then show that a definition which is appropriate for one use of the word would not be appropriate for the second use.
	www.geocities.com /phineasbg/kirklogic.html (15724 words)

	Margaret M. Fleck
		Popular for proofs of the existence of God and for proofs that computers cannot think.
		Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
		Among the many proponents of this theory, we have found one who is obviously loony; so we can discredit the entire theory.
	www.cs.hmc.edu /~fleck/proof.html (627 words)

	Living Proof \| lawrence.com
		By Frank Tankard / Monday, Aug. 13, 2007
		Junctures of triumph and calamity, love and melancholy and confusion, decision and fog, guilt and embarrassment and shame, euphoria and exhaustion.
		It could be the point on the teeter-totter where a person starts to fall, or to get back up again.
	www.lawrence.com /volunteer (765 words)

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