Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 15, Issue 4 (Jan 2007)

Issues

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

Hiroshi Yamazaki / Noboru Endou / Yasunari Shidama / Hiroyuki Okazaki
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-007-0026-3

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

In 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.

  • [4] Józef Białas. The σ-additive measure theory. Formalized Mathematics, 2(2):263-270, 1991.Google Scholar

  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Google Scholar

  • [8] Czesław Byliński and Piotr Rudnicki. Bounding boxes for compact sets in ε2. Formalized Mathematics, 6(3):427-440, 1997.Google Scholar

  • [9] Noboru Endou and Yasunari Shidama. Integral of measurable function. Formalized Mathematics, 14(2):53-70, 2006.Google Scholar

  • [10] Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definitions and basic properties of measurable functions. Formalized Mathematics, 9(3):495-500, 2001.Google Scholar

  • [11] Adam Grabowski. On the Kuratowski limit operators. Formalized Mathematics, 11(4):399-409, 2003.Google Scholar

  • [12] Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.Google Scholar

  • [13] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Google Scholar

  • [14] Jarosław Kotowicz. Monotone real sequences. Subsequences. Formalized Mathematics, 1(3):471-475, 1990.Google Scholar

  • [15] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Google Scholar

  • [16] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.Google Scholar

  • [17] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.Google Scholar

  • [18] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.Google Scholar

  • [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

  • [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

  • [22] Bo Zhang, Hiroshi Yamazaki, and Yatsuka Nakamura. Inferior limit and superior limit of sequences of real numbers. Formalized Mathematics, 13(3):375-381, 2005.Google Scholar

  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Google Scholar

  • [2] Józef Białas. Infimum and supremum of the set of real numbers. Measure theory. Formalized Mathematics, 2(1):163-171, 1991.Google Scholar

  • [3] Józef Białas. Series of positive real numbers. Measure theory. Formalized Mathematics, 2(1):173-183, 1991.Google Scholar

About the article


Published Online: 2008-06-09

Published in Print: 2007-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0026-3.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama
Formalized Mathematics, 2009, Volume 17, Number 2
[2]
Noboru Endou, Keiko Narita, and Yasunari Shidama
Formalized Mathematics, 2008, Volume 16, Number 4
[3]
Noboru Endou, Keiko Narita, and Yasunari Shidama
Formalized Mathematics, 2008, Volume 16, Number 2
[4]
Noboru Endou, Yasunari Shidama, and Keiko Narita
Formalized Mathematics, 2008, Volume 16, Number 1
[5]
Keiko Narita, Noboru Endou, and Yasunari Shidama
Formalized Mathematics, 2009, Volume 17, Number 2

Comments (0)

Please log in or register to comment.
Log in