Indirect Proof

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indirect proof

[‚in·də‚rekt ′pr¨f]
(mathematics)
A proof of a proposition in which another theorem is first proven from which the given theorem follows.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Indirect Proof

the proof in logic of a proposition (thesis), based on the refutation (that is, proof of falsity, proof of negation) of certain other propositions that have certain relations with the thesis.

In what is referred to as partitive indirect proof the thesis is one of the terms of a disjunction (propositions of the form “A1, or A2, or …, or, An”) that is known to be true (or is assumed to have been previously proved); the proof itself consists of refuting all members AI of this disjunction except the one being proved. Apagogic indirect proof, or adversive proof, consists of refuting the negation of the thesis to be proved (”antithesis”). If one assumes the truth (or demonstrableness) of the principle of the excluded middle (“A or not-A”), then apagogic indirect proof may be considered to be a particular case of the partitive method.