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Using linear logic to reason about sequent systems
Using linear logic to reason about sequent systems

Proof by Induction
Proof by Induction

Carmichael numbers with three prime factors
Carmichael numbers with three prime factors

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In order to define the notion of proof rigorously, we would have to
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Proof of the Fundamental Theorem of Algebra

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WE’VE GOT COOL MATH! MARCH 2013 CURIOUS MATHEMATICS FOR FUN AND JOY

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Introduction to Logic

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Chapter 2 Propositional Logic

Extracting Proofs from Tabled Proof Search
Extracting Proofs from Tabled Proof Search

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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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