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Pole DC | Wartość | Język |
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dc.contributor.author | Bancerek, Grzegorz | - |
dc.date.accessioned | 2015-12-02T18:01:48Z | - |
dc.date.available | 2015-12-02T18:01:48Z | - |
dc.date.issued | 2009 | - |
dc.identifier.citation | Formalized Mathematics, Volume 17, Issue 4, 2009, Pages 249-256 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.issn | 1898-9934 | - |
dc.identifier.uri | http://hdl.handle.net/11320/3552 | - |
dc.description.abstract | An epsilon number is a transfinite number which is a fixed point of an exponential map: ωϵ = ϵ. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: and for limit ordinal λ: Tetration stabilizes at ω: Every ordinal number α can be uniquely written as where κ is a natural number, n1, n2, …, nk are positive integers, and β1 > β2 > … > βκ are ordinal numbers (βκ = 0). This decomposition of α is called the Cantor Normal Form of α. | - |
dc.language.iso | en | - |
dc.publisher | De Gruyter Open | - |
dc.title | Epsilon Numbers and Cantor Normal Form | - |
dc.type | Article | - |
dc.identifier.doi | 10.2478/v10037-009-0032-8 | - |
dc.description.Affiliation | Białystok Technical University, Poland | - |
dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | - |
dc.description.references | Grzegorz Bancerek. Increasing and continuous ordinal sequences. Formalized Mathematics, 1(4):711-714, 1990. | - |
dc.description.references | Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990. | - |
dc.description.references | Grzegorz Bancerek. Ordinal arithmetics. Formalized Mathematics, 1(3):515-519, 1990. | - |
dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. | - |
dc.description.references | Grzegorz Bancerek. Sequences of ordinal numbers. Formalized Mathematics, 1(2):281-290, 1990. | - |
dc.description.references | Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. | - |
dc.description.references | Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. | - |
dc.description.references | Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001. | - |
dc.description.references | Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2009, Volume 17, Issue 4 |
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v10037-009-0032-8.pdf | 269,87 kB | Adobe PDF | Otwórz |
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