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In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with science obtaining its evidence from nature, [11] law obtaining its evidence from witnesses and forensic investigation, [12] and so on. A notable exception is mathematics, whose proofs are drawn from a mathematical ...
The legal term "probity" means authority or credibility, the power of testimony to prove facts when given by persons of reputation or status. [ 6 ] Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. [ 7 ]
Proof of concept testing of oil cleanup equipment. Proof of concept (POC or PoC), also known as proof of principle, is a realization of a certain idea, method or principle in order to demonstrate its feasibility, [1] or viability, [2] or a demonstration in principle with the aim of verifying that some concept or theory has practical potential.
Proof complexity, computational resources required to prove statements; Proof procedure, method for producing proofs in proof theory; Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects; Statistical proof, demonstration of degree of certainty for a hypothesis
The alternative origin given is that the word "prove" is used in the archaic sense of "test", [3] a reading advocated, for example, by a 1918 Detroit News style guide: The exception proves the rule is a phrase that arises from ignorance, though common to good writers. The original word was preuves, which did not mean proves but tests. [4]
As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases. In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry . [ 2 ]
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An alternative is to prove the disjunction "(P and Q) or (not-P and not-Q)", which itself can be inferred directly from either of its disjuncts—that is, because "iff" is truth-functional, "P iff Q" follows if P and Q have been shown to be both true, or both false.