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Goodstein's theorem

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence (as defined below) eventually terminates at 0. Laurence Kirby and Jeff Paris showed in 1982 that Goodstein's theorem is unprovable in Peano arithmetic (but it can be proven in stronger…

Applications, Proof of Goodstein's theorem & Overview

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Overview

Hereditary base-n notation

Goodstein sequences

Proof of Goodstein's theorem

Sequence length as a function of the starting value

Application to computable functions

Bibliography

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Goodstein's theorem

Nodes53
Edges52
Triples47
Avg. degree1.96
Density0.037736
Components1

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Goodstein's theorem

Top relations

related to External links · 23
Goodstein's theorem → Dan Kaplan, Detour, Eric, Franklan, Goodstein, Goodstein Calculator Archived, Goodstein Sequence, Goodstein Sequences, Goodstein's, Haskell, Infinity, Justin, Marshall College LibraryDefinition, MathWorld, MillerA Classification, PA, Peano Arithmetic, Sequences, Some, The Power
related to Proof of Goodstein's theorem · 11
Goodstein's theorem → Actually, By, Cantor, For, Given, Goodstein, Goodstein's, Peano, The, Then, We
related to Application to computable functions · 8
Goodstein's theorem → Because, But, Goodstein, Goodstein's, Peano, The Goodstein, This, Turing
related to Hereditary base-n notation · 4
Goodstein's theorem → Goodstein, Goodstein's, This, To
is a · 1
Goodstein's theorem → statement about the natural numbers

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Important terminology

displaystyle goodstein sequence theorem goodstein's arithmetic peano paris proof example terminates kirby notation hereditary sequences number every function base numbers

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Goodstein's theoremis astatement about the natural numbers0.90text
Goodstein's theoremrelated to Application to computable functionsGoodstein's0.60section
Goodstein's theoremrelated to Application to computable functionsPeano0.60section
Goodstein's theoremrelated to Application to computable functionsThe Goodstein0.60section
Goodstein's theoremrelated to Application to computable functionsTuring0.60section
Goodstein's theoremrelated to Application to computable functionsGoodstein0.60section
Goodstein's theoremrelated to Application to computable functionsThis0.60section
Goodstein's theoremrelated to Application to computable functionsBecause0.60section
Goodstein's theoremrelated to Application to computable functionsBut0.60section
Goodstein's theoremrelated to External linksWeisstein0.60section
Goodstein's theoremrelated to External linksEric0.60section
Goodstein's theoremrelated to External linksGoodstein Sequence0.60section

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