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.

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.

References in periodicals archive ?
Nevertheless, Baroco has a potential inferential necessity, and thereby is an incomplete deduction, because there is an indirect proof through impossibility, which reduces Baroco to the complete deduction Barbara.
Indirect proof of the failure of the ERP promise also lies in the widespread use of ETL (Extract, Transform, Load) and related business intelligence applications.
For example in Figure 1, the student is currently deriving the formula "C," using the rule "Indirect Proof" using the formulae of lines 2 and 7.
Stephens thus reads early witchcraft theorists' writing in different genres as attempting to overcome widespread theological anxiety: "[Jean] Vineti provides some of the earliest evidence that the existence of witches was vehemently defended because it gave indirect proof of the existence of God by proving that other spirits were real" (25).
In short, while the exhibition offered indirect proof of Wigley's own admission that the selected architects did not "participate in any new movement," the projects, taken collectively, stood firmly on the side of a continuing "tradition" of the modern.
If Lemon had skimmed from sales, there would be only indirect proof of her crime through falling revenue and/or rising costs.
Her courtroom explanation of the "net-worth method of indirect proof' was directly responsible for the justice Department's victory in prosecuting two groundbreaking criminal tax cases in Colorado involving hidden income.
(1997), thus giving an indirect proof to Weir's formula.
While heartening to those who believe planetary systems are widespread, these discoveries have provided only indirect proof of planets.
This claim is advanced by a kind of indirect proof: Selection can't possibly do all the marvelous things it would have to generate the order we see in the world, so what's left must be the result of spontaneous order.
Indirect proof of the complexity of the casting process is that most foundries accept scrap rates of 5% or higher and that several test pours have to be made before a new pattern is used for production runs.
More generally we shed some light on the specific details and peculiarities of the indirect proof structure, some of which are often left unattended whilst studying and practising proof techniques.