proof (redirected from proof beyond a reasonable doubt)

proof, in mathematics

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.

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proof, in printing

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).

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proof, in law

proof, in law: see evidence.

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proof

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 n = 1 and can be shown to hold for n = k + 1 whenever n = k (a constant) is also true, then it holds for all values of n. An example is the assertion that the sum of the first n counting numbers is n(n + 1)/2.

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proof

1. Law the whole body of evidence upon which the verdict of a court is based

2. Maths logic a sequence of steps or statements that establishes the truth of a proposition

3. Scots law trial before a judge without a jury

4. (in engraving, etc.) a print made by an artist or under his supervision for his own satisfaction before he hands the plate over to a professional printer

5. Photog a trial print from a negative

6. 

a. the alcoholic strength of proof spirit

b. the strength of a beverage or other alcoholic liquor as measured on a scale in which the strength of proof spirit is 100 degrees

7. having the alcoholic strength of proof spirit

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proof [prüf]

(engineering)

Reproduction of a die impression by means of a cast.

(food engineering)

The strength of the ethyl alcohol in distilled spirits; in the United States, each degree of proof is equal to 0.5% of alcohol by volume.

To activate yeast by mixing it with water or milk and letting the mixture stand for a given period of time.

(graphic arts)

The inked impression of composed type or a plate; used for inspection purposes or for pasting up with other artwork.

(mathematics)

A deductive demonstration of a mathematical statement.

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1.	(logic)	proof - A finite sequence of well-formed formulas, F1, F2, ... Fn, where each Fi either is an axiom, or follows by some rule of inference from some of the previous F's, and Fn is the statement being proved. See also proof theory.
2.		proof - A left-associative natural language parser by Craig R. Latta <latta@xcf.berkeley.edu>. Ported to Decstation 3100, Sun-4. ftp://scam.berkeley.edu/pub/src/local/proof/. E-mail: <proof@xcf.berkeley.edu>. Mailing list: proof-requestf@xcf.berkeley.edu (Subject: add me).