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Methods of Proof
Methods of Proof

Notes
Notes

... If dealing with a finite domain in which the proof is to be shown to be valid, then using the exhaustive proof technique, one can go over all the possible cases for each member of the finite domain. Final result of this exercise: you prove or disprove the theorem but you could be definitely exhauste ...
Flexible Logo plots of symbols and alphanumeric
Flexible Logo plots of symbols and alphanumeric

Flexible Logo plots of symbols and alphanumeric
Flexible Logo plots of symbols and alphanumeric

Name
Name

Soundness and completeness
Soundness and completeness

... provable in ND. As with most logics, the completeness of propositional logic is harder (and more interesting) to show than the soundness. We shall spend the next few slides with the completeness proof. ...
userfiles/SECTION F PROOF BY CONTRADICTION
userfiles/SECTION F PROOF BY CONTRADICTION

... Let P be another proposition ‘every non-zero real number has a unique reciprocal’. Then ( not P ) is ‘there is a non-zero real number whose reciprocal is not unique’. What does this mean? There is a number (not zero) which has more than one reciprocal. We will do an example involving reciprocals in ...
CS311H: Discrete Mathematics Mathematical Proof Techniques
CS311H: Discrete Mathematics Mathematical Proof Techniques

overhead 7/conditional proof [ov]
overhead 7/conditional proof [ov]

On the computational content of intuitionistic propositional proofs
On the computational content of intuitionistic propositional proofs

Chapter 8: The Logic of Conditionals
Chapter 8: The Logic of Conditionals

HONEST ELEMENTARY DEGREES AND DEGREES OF RELATIVE
HONEST ELEMENTARY DEGREES AND DEGREES OF RELATIVE

A Mathematical Analysis of Akan Adinkra Symmetry
A Mathematical Analysis of Akan Adinkra Symmetry

... structures that have internal consistency. For a mathematical structure to be classified as a group, it has to satisfy certain conditions. There is an operation which when performed on one member of the group gives a result that points to another member of the group. There are also the concepts of a ...
gödel`s completeness theorem with natural language formulas
gödel`s completeness theorem with natural language formulas

CS151 Spring 2010 Lecture 12
CS151 Spring 2010 Lecture 12

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(425.0kB )

Section 1.4 Mathematical Proofs
Section 1.4 Mathematical Proofs

Reduced decompositions of permutations in terms of star
Reduced decompositions of permutations in terms of star

pythagoreantreasury[1]
pythagoreantreasury[1]

Pythagorean Treasury Powerpoint - 8.1 ~ A collection of teaching
Pythagorean Treasury Powerpoint - 8.1 ~ A collection of teaching

Discrete Mathematics I Lectures Chapter 4
Discrete Mathematics I Lectures Chapter 4

PPT - School of Computer Science
PPT - School of Computer Science

Basic Proof Techniques
Basic Proof Techniques

Gödel on Conceptual Realism and Mathematical Intuition
Gödel on Conceptual Realism and Mathematical Intuition

computability by probabilistic turing machines
computability by probabilistic turing machines

< 1 ... 4 5 6 7 8 9 10 11 12 ... 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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