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Such a proof is again a refutation by contradiction. A typical example is the proof of the proposition "there is no smallest positive rational number": assume there is a smallest positive rational number q and derive a contradiction by observing that q / 2 is even smaller than q and still positive.
Reductio ad absurdum, painting by John Pettie exhibited at the Royal Academy in 1884. In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one."
A technical argument by a trusted author, which is hard to check and looks similar to arguments known to be correct, is hardly ever checked in detail. Vladimir Voevodsky, [ 1 ] This page lists notable examples of incomplete or incorrect published mathematical proofs .
Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. [7] It is likely that the idea of demonstrating a conclusion first arose in connection with geometry, which originated in practical problems of land measurement. [8]
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...
The circular argument, in which the proof of some proposition presupposes the truth of that very proposition; The regressive argument, in which each proof requires a further proof, ad infinitum; The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended
Proof by intimidation (or argumentum verbosum) is a jocular phrase used mainly in mathematics to refer to a specific form of hand-waving whereby one attempts to advance an argument by giving an argument loaded with jargon and obscure results or by marking it as obvious or trivial. [1]