com Henry Cate How to prove

Found at: 0x1bi.net:70/textfiles/file?humor/proof.met

```From cate3.osbunorth@xerox.com Fri Aug 31 19:33:53 1990
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```From: cate3.osbunorth@xerox.com (Henry Cate III)
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```Subject: How to prove something
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```----------------------------------------------------
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```Survey of proof techniques
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```This survey was written by Dana Angluin.  Not really sure where it came from.
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```  The author gives only the case n=2 and suggests that it contains most
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```  of the ideas of the general proof.
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```  'Trivial.'
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```  Works well in a classroom or seminar setting.
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```  Best done with access to at least four alphabets and special symbols.
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```  An issue or two of a journal devoted to your proof is useful.
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```  'The reader may easily supply the details.'
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```  'The other 253 cases are analogous.'
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```  '...'
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```  A long plotless sequence of true and\or meaningless syntactically related
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```  statements.
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```  The author cites the negation, converse, or generalization of a theorem
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```  from the literature to support his claims.
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```  How could three different government agencies be wrong?
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```  'I saw Karp in the elevator and he said it was probably NP-complete.'
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```  'Eight-dimensional colored cycle stripping is NP-complete [Karp, personal
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```  commmunication].
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```
```
```  'To see that infinite-dimensional colored cycle stripping is decidable,
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```  we reduce it to the halting problem.'
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```  The author cites a simple corollary of a theorem to be found in a privately
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```  circulated memoir of the Slovenian Philological Society, 1883.
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```  A large body of useful consequences all follow from the proposition in
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```  question.
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```  Long and diligent search has not revealed a counterexample.
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```  The negation of the proposition is unimaginable or meaningless.  Popular
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```  for proofs of the existence of God.
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```  In reference A, Theorem 5 is said to follow from Theorem 3 in reference B,
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```  which is shown to follow from Corollary 6.2 in reference C, which is an
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```  easy consequence of Theorem 5 in reference A.
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```  A method is given to construct the desired proof.  The correctness of the
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```  method is proved by any of these techniques.
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```  A more convincing form of proof by example.  Combines well with proof by
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```  omission.
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```  It is useful to have some kind of authority relation to the audience.
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```  Nothing even remotely resembling the cited theorem appears in the reference
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```  given.
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```  Reference is usually to a forthcoming paper of the author, which is often
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```  not as forthcoming as at first.
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```  Some standard but inconvenient definitions are changed for the statement
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```  of the result.
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```  Cloud-shaped drawings frequently help here.
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```----------------------------------------------------
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```Henry Cate III
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```--------------
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```  (ucbvax!xerox.com!cate3.osbunorth)  OR  (cate3.osbunorth@Xerox.Com)
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```Everyone complains of his memory, no one of his judgment.
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