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... Proof Strategies for proving p → q — Choose a method. 1. First try a direct method of proof. 2. If this does not work, try an indirect method (e.g., try to prove the contrapositive). — For whichever method you are trying, choose a strategy. 1. First try forward reasoning. Start with the axioms ...
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... Used when exhaustive proof doesn’t work. Using the rules of propositional and predicate logic, prove P  Q. Hence, assume the hypothesis P and prove Q. Hence, a formal proof would consist of a proof sequence to go from P to Q. Consider the conjecture x is an even integer Λ y is an even integer  the ...
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< 1 ... 5 6 7 8 9 10 11 12 13 ... 23 >

Turing's proof

Turing's proof is a proof by Alan Turing, first published in January 1937 with the title On Computable Numbers, With an Application to the Entscheidungsproblem. It was the second proof of the assertion (Alonzo Church's proof was first) that some decision problems are ""undecidable"": there is no single algorithm that infallibly gives a correct ""yes"" or ""no"" answer to each instance of the problem. In his own words:""...what I shall prove is quite different from the well-known results of Gödel ... I shall now show that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]..."" (Undecidable p. 145).Turing preceded this proof with two others. The second and third both rely on the first. All rely on his development of type-writer-like ""computing machines"" that obey a simple set of rules and his subsequent development of a ""universal computing machine"".
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