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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 ...
false (contradiction) bottom, falsity, contradiction, falsum, empty clause propositional logic, Boolean algebra, first-order logic: denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines.
In mathematics, the symbol used to represent a contradiction within a proof varies. [7] Some symbols that may be used to represent a contradiction include ↯, Opq, , ⊥, / , and ※; in any symbolism, a contradiction may be substituted for the truth value "false", as symbolized, for instance, by "0" (as is common in Boolean algebra).
Proofs employ logic expressed in mathematical symbols, ... this takes the form of a proof by contradiction in which the nonexistence of the object is proved to be ...
A symbol used in logic to represent falsity or a contradiction, often denoted as . "Fido"-Fido principle The principle in philosophy of language suggesting that the meaning of a word is the object it refers to, exemplified by the idea that the meaning of "Fido" is the dog Fido itself.
This resolution technique uses proof by contradiction and is based on the fact that any sentence in propositional logic can be transformed into an equivalent sentence in conjunctive normal form. [4] The steps are as follows. All sentences in the knowledge base and the negation of the sentence to be proved (the conjecture) are conjunctively ...
Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq". The tee symbol is sometimes used to denote an arbitrary tautology, with the dual symbol representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1".
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.