Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorBancerek, Grzegorz-
dc.identifier.citationFormalized Mathematics, Volume 17, Issue 4, 2009, Pages 249-256-
dc.description.abstractAn 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.publisherDe Gruyter Open-
dc.titleEpsilon Numbers and Cantor Normal Form-
dc.description.AffiliationBiałystok Technical University, Poland-
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.-
dc.description.referencesGrzegorz Bancerek. Increasing and continuous ordinal sequences. Formalized Mathematics, 1(4):711-714, 1990.-
dc.description.referencesGrzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.-
dc.description.referencesGrzegorz Bancerek. Ordinal arithmetics. Formalized Mathematics, 1(3):515-519, 1990.-
dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.-
dc.description.referencesGrzegorz Bancerek. Sequences of ordinal numbers. Formalized Mathematics, 1(2):281-290, 1990.-
dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.-
dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.-
dc.description.referencesTetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.-
dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.-
Występuje w kolekcji(ach):Formalized Mathematics, 2009, Volume 17, Issue 4

Pliki w tej pozycji:
Plik Opis RozmiarFormat 
v10037-009-0032-8.pdf269,87 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons