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\title{Proof Methods}
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\twocolumn[
\begin{center}\begin{Large}Proof Methods\end{Large}\end{center}
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\begin{description}
  \item[by example] : \\
    The author gives only the case n = 2 and suggests that it contains most
    of the ideas of the general proof.
  \item[by intimidation] : \\
    `Trivial.'
  \item[by vigorous handwaving] : \\
    Works well in a classroom or seminar setting.
  \item[by cumbersome notation] : \\
    Best done with access to at least four alphabets and special symbols.
  \item[by exhaustion] : \\
    An issue or two of a journal devoted to your proof is useful.
  \item[by omission] : \\
    `The reader may easily supply the details.' \\
    `The other 253 cases are analogous.' \\
    `...'
  \item[by obfuscation] : \\
    A long plotless sequence of true and/or meaningless syntactically
    related statements.
  \item[by wishful citation] : \\
    The author cites the negation, converse, or generalization of a theorem
    from literature to support his claims.
  \item[by funding] : \\
    How could three different government agencies be wrong?
  \item[by eminent authority] : \\
    `I saw Karp in the elevator and he said it was probably NP-complete.'
  \item[by personal communication] : \\
    `Eight-dimensional colored cycle stripping is NP-complete 
    [Karp,personal communication].'
  \item[by reduction to the wrong problem] : \\
    `To see that infinite-dimensional colored cycle stripping is decidable,
    we reduce it to the halting problem.'
  \item[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.
  \item[by importance] : \\
    A large body of useful consequences all follow from the proposition in
    question.
  \item[by accumulated evidence] : \\
    Long and diligent search has not revealed a counterexample.
  \item[by cosmology] : \\
    The negation of the proposition is unimaginable or meaningless. Popular
    for proofs of the existence of God.
  \item[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.
  \item[by metaproof] : \\
    A method is given to construct the desired proof. The correctness of
    the method is proved by any of these techniques.
  \item[by picture] : \\
    A more convincing form of by example. Combines well with by
    omission.
  \item[by vehement assertion] : \\
    It is useful to have some kind of authority in relation to the audience.
  \item[by ghost reference] : \\
    Nothing even remotely resembling the cited theorem appears in the
    reference given.
  \item[by forward reference] : \\
    Reference is usually to a forthcoming paper of the author, which is
    often not as forthcoming as at first.
  \item[by semantic shift] : \\
    Some standard but inconvenient definitions are changed for the
    statement of the result.
  \item[by appeal to intuition] : \\
    Cloud-shaped drawings frequently help here.
\end{description}

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