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In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...
Unlike standard Vieta jumping, constant descent is not a proof by contradiction, and it consists of the following four steps: [10] The equality case is proven so that it may be assumed that a > b . b and k are fixed and the expression relating a , b , and k is rearranged to form a quadratic with coefficients in terms of b and k , one of whose ...
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]
[6] 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, a minimal counterexample is the smallest example which falsifies a claim, and a proof by minimal counterexample is a method of proof which combines the use of a minimal counterexample with the ideas of proof by induction and proof by contradiction.
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.