.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.
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