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- Graham's_number abstract "Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a problem in Ramsey theory.The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977, writing that Graham had recently established, in an unpublished proof, "a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof." The 1980 Guinness Book of World Records repeated Gardner's claim, adding to the popular interest in this number. According to physicist John Baez, Graham invented the quantity now known as Graham's number in conversation with Gardner himself. While Graham was trying to explain a result in Ramsey theory which he had derived with his collaborator B. L. Rothschild, Graham found that the quantity now known as Graham's number was easier to explain than the actual number appearing in the proof. Because the number which Graham described to Gardner is larger than the number in the paper itself, both are valid upper bounds for the solution to the Ramsey-theory problem studied by Graham and Rothschild.Graham's number is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes' number and Moser's number. Indeed, like the last three of those numbers, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume. Even power towers of the form are beyond useless for this purpose, although it can be easily described by recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Graham. The last ten digits of Graham's number are ...2464195387.Specific integers known to be far larger than Graham's number have since appeared in many serious mathematical proofs (e.g., in connection with Friedman's various finite forms of Kruskal's theorem).".
- Graham's_number thumbnail GrahamCube.svg?width=300.
- Graham's_number wikiPageExternalLink cubes.html.
- Graham's_number wikiPageExternalLink GrahamsNumber.html.
- Graham's_number wikiPageExternalLink graham.htm.
- Graham's_number wikiPageExternalLink pre_cube.pdf.
- Graham's_number wikiPageID "234232".
- Graham's_number wikiPageRevisionID "606185793".
- Graham's_number hasPhotoCollection Graham's_number.
- Graham's_number subject Category:Integers.
- Graham's_number subject Category:Large_integers.
- Graham's_number subject Category:Large_numbers.
- Graham's_number subject Category:Ramsey_theory.
- Graham's_number type Abstraction100002137.
- Graham's_number type Battalion113775093.
- Graham's_number type DefiniteQuantity113576101.
- Graham's_number type IndefiniteQuantity113576355.
- Graham's_number type Integer113728499.
- Graham's_number type Integers.
- Graham's_number type LargeIndefiniteQuantity113757724.
- Graham's_number type LargeInteger113745420.
- Graham's_number type LargeIntegers.
- Graham's_number type LargeNumbers.
- Graham's_number type Measure100033615.
- Graham's_number type Number113582013.
- Graham's_number comment "Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a problem in Ramsey theory.The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977, writing that Graham had recently established, in an unpublished proof, "a bound so vast that it holds the record for the largest number ever used in a serious mathematical proof." The 1980 Guinness Book of World Records repeated Gardner's claim, adding to the popular interest in this number. ".
- Graham's_number label "Getal van Graham".
- Graham's_number label "Graham's number".
- Graham's_number label "Grahams Zahl".
- Graham's_number label "Liczba Grahama".
- Graham's_number label "Nombre de Graham".
- Graham's_number label "Numero di Graham".
- Graham's_number label "Número de Graham".
- Graham's_number label "Número de Graham".
- Graham's_number label "Число Грэма".
- Graham's_number label "عدد غراهام (رياضيات)".
- Graham's_number label "グラハム数".
- Graham's_number label "葛立恆數".
- Graham's_number sameAs Grahams_Zahl.
- Graham's_number sameAs Número_de_Graham.
- Graham's_number sameAs Nombre_de_Graham.
- Graham's_number sameAs Numero_di_Graham.
- Graham's_number sameAs グラハム数.
- Graham's_number sameAs 그레이엄_수.
- Graham's_number sameAs Getal_van_Graham.
- Graham's_number sameAs Liczba_Grahama.
- Graham's_number sameAs Número_de_Graham.
- Graham's_number sameAs m.01j0tx.
- Graham's_number sameAs Q733169.
- Graham's_number sameAs Q733169.
- Graham's_number sameAs Graham's_number.
- Graham's_number wasDerivedFrom Graham's_number?oldid=606185793.
- Graham's_number depiction GrahamCube.svg.
- Graham's_number isPrimaryTopicOf Graham's_number.
