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  3. Formalized Mathematics
  4. Formalized Mathematics, 2007, Volume 15, Issue 4

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21416
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    Pole DCWartośćJęzyk
    dc.contributor.authorYamazaki, Hiroshi-
    dc.contributor.authorEndou, Noboru-
    dc.contributor.authorShidama, Yasunari-
    dc.contributor.authorOkazaki, Hiroyuki-
    dc.date.accessioned2026-11-04T08:52:16Z-
    dc.date.available2026-11-04T08:52:16Z-
    dc.date.issued2007-
    dc.identifier.citationFormalized Mathematics, Volume 15, Issue 4, Pages 231-235pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/21416-
    dc.description.abstractIn this article, we extended properties of sequences of real numbers to sequences of extended real numbers. We also introduced basic properties of the inferior limit, superior limit and convergence of sequences of extended real numbers.pl
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsCC BY-SA 4.0-
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
    dc.titleInferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numberspl
    dc.typeArticlepl
    dc.rights.holder© 2008 Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, Hiroyuki Okazaki, published by University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.identifier.doi10.2478/v10037-007-0026-3-
    dc.description.AffiliationHiroshi Yamazaki - Shinshu University, Nagano, Japanpl
    dc.description.AffiliationNoboru Endou - Gifu National College of Technology, Japanpl
    dc.description.AffiliationYasunari Shidama - Shinshu University, Nagano, Japanpl
    dc.description.AffiliationHiroyuki Okazaki - Shinshu University, Nagano, Japanpl
    dc.description.referencesJózef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
    dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.pl
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.pl
    dc.description.referencesCzesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.pl
    dc.description.referencesNoboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.pl
    dc.description.referencesNoboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.pl
    dc.description.referencesAdam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.pl
    dc.description.referencesJarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.pl
    dc.description.referencesJarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.pl
    dc.description.referencesJarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.pl
    dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.pl
    dc.description.referencesAndrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.pl
    dc.description.referencesAndrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.pl
    dc.description.referencesAndrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.pl
    dc.description.referencesBo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Inferior limit and superior limit of sequences of real numbers. Formalized Mathematics, 13(3):375-381, 2005.pl
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.pl
    dc.description.referencesJózef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.pl
    dc.description.referencesJózef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.pl
    dc.description.volume15pl
    dc.description.issue4pl
    dc.description.firstpage231pl
    dc.description.lastpage235pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Formalized Mathematics, 2007, Volume 15, Issue 4

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