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PROOF
, in mathematics

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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The Columbia Encyclopedia, Sixth Edition Copyright© 2004, Columbia University Press. Licensed from Lernout & Hauspie Speech Products N.V. All rights reserved.

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Publication Information: Encyclopedia Article Title: Proof, in Mathematics. Encyclopedia Title: The Columbia Encyclopedia, Sixth Edition. Publisher: Columbia University Press. Place of Publication: New York. Publication Year: 2004.
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