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proof, in law: see evidence.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

proof, in mathematics, finite sequence of propositions each of which is either an axiom or follows from preceding propositions by one of the rules of logical inference (see symbolic logic). Mathematical proofs are quite distinct from inductive, statistical, heuristic, analogical, and other types of reasoning or persuasion that are sometimes accepted as proofs in other fields of science or human affairs. Proof theory has developed into one of the important branches of modern mathematical logic. Some schools of mathematical logic reject certain methods in proofs, such as use of the law of excluded middle (either *p* is true or *p* is false) or of mathematical definitions involving properties that are not effectively verifiable.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

proof, in printing, a trial impression for inspection. **Proofreading** is the inspection and marking of proof for correction of errors and imperfections. Proofreaders' marks are included in dictionaries. Directions for proofreading are given in several sources including *The Chicago Manual of Style,* published by the Univ. of Chicago Press (15th ed. 2003); *Words into Type,* by M. E. Skillin and R. M. Gay (3d ed. 1974); and *The Fine Art of Copyediting,* by E. M. Stainton (1991).

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

In logic and mathematics, an argument that establishes a proposition's validity. Formally, it is a finite sequence of formulas generated according to accepted rules. Each formula either is an axiom or is derived from a previously established theorem, and the last formula is the statement that is to be proven. The essence of deductive reasoning (*see* deduction), this is the basis of Euclidean geometry and all scientific methods inspired by it. An alternative form of proof, called mathematical induction, applies to propositions defined through processes based on the counting numbers. If the proposition holds for *math.n* = 1 and can be shown to hold for *math.n* = *math.k* + 1 whenever *math.n* = *math.k* (a constant) is also true, then it holds for all values of *math.n*. An example is the assertion that the sum of the first *math.n* counting numbers is *math.n*(*math.n* + 1)/2.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Proof may refer to:

- A rigorous, compelling argument
- Formal proof
- Mathematical proof
- Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects
- Logical argument
- Evidence (law), tested evidence or a legal proof
- Various kinds of testing, checking, or measuring
- Proofing (baking technique), the process by which a yeast-leavened dough rises, also called “proving”
- Proofreading
- Artist's proof, a single print taken during the printmaking process
- Proof coinage, a coin made as an example of a particular strike
- Proof test, for a firearm
- Homeopathic proving, testing a substance's effect on the body
- Galley proof, a preliminary version of a publication
- Proof (alcohol), a measure of an alcoholic drink’s strength
- In entertainment
- Proof (1991 film), an Australian film by Jocelyn Moorhouse
- Proof (play), a play by David Auburn
- Proof (2005 film), a film directed by John Madden, based on the play
- "Proof", a B-side by the band Coldplay, off their single Speed of Sound
- "Proof", a song by Paul Simon from his 1990 album The Rhythm of the Saints
- "Proof", a song by Happy Rhodes from her 1998 album Many Worlds Are Born Tonight
- "Proof", a 2004 song by J-pop group angela
- "Proof", a 2007 song by Japanese artist Mell
- Proof (rapper), a deceased member of D12
- Proof (comics), a comic series from Image Comics

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Last updated on Saturday September 20, 2008 at 18:49:22 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Saturday September 20, 2008 at 18:49:22 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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