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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]
As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as reductio ad absurdum. This amounts to finding an area of a ...
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 ...
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.
If the form of the contradiction is that we can derive a further counterexample D, that is smaller than C in the sense of the working hypothesis of minimality, then this technique is traditionally called proof by infinite descent. In which case, there may be multiple and more complex ways to structure the argument of the proof.
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 ...