proof, in mathematics

proof, in mathematics, finite sequence of propositions each of which is either an axiom axiom, in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). Examples of axioms used widely in mathematics are those related to equality (e.g.
..... Click the link for more information. or follows from preceding propositions by one of the rules of logical inference (see symbolic logic symbolic logic or mathematical logic, formalized system of deductive logic, employing abstract symbols for the various aspects of natural language.
..... Click the link for more information. ). 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.

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).

proof, in law

proof, in law: see evidence evidence, in law, material submitted to a judge or a judicial body to resolve disputed questions of fact. The rules discussed in this article were developed in England for use in jury trials.
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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.

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).