## Summary

Double sequences are important extension of the ordinary notion of a sequence. In this article we formalized three types of limits of double sequences and the theory of these limits.

Show Summary Details# Formalized Mathematics

### (a computer assisted approach)

#### Open Access

# Double Sequences and Limits

## Summary

## Comments (0)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2015: 0.134

Source Normalized Impact per Paper (SNIP) 2015: 0.686

Impact per Publication (IPP) 2015: 0.296

Noboru Endou / Hiroyuki Okazaki / Yasunari Shidama

Double sequences are important extension of the ordinary notion of a sequence. In this article we formalized three types of limits of double sequences and the theory of these limits.

Keywords: formalization of basic metric space; limits of double sequences

[1] Grzegorz Bancerek. The fundamental properties of natural numbers.

*Formalized Mathematics*, 1(1):41-46, 1990.[2] Grzegorz Bancerek. The ordinal numbers.

*Formalized Mathematics*, 1(1):91-96, 1990.[3] Czesław Bylinski. Binary operations.

*Formalized Mathematics*, 1(1):175-180, 1990.[4] Czesław Bylinski. The complex numbers.

*Formalized Mathematics*, 1(3):507-513, 1990.[5] Czesław Bylinski. Binary operations applied to finite sequences.

*Formalized Mathematics*, 1(4):643-649, 1990.[6] Czesław Bylinski. Functions and their basic properties.

*Formalized Mathematics*, 1(1): 55-65, 1990.[7] Czesław Bylinski. Functions from a set to a set.

*Formalized Mathematics*, 1(1):153-164, 1990.[8] Czesław Bylinski. Partial functions.

*Formalized Mathematics*, 1(2):357-367, 1990.[9] Czesław Bylinski. Some basic properties of sets.

*Formalized Mathematics*, 1(1):47-53, 1990.[10] Noboru Endou, Keiko Narita, and Yasunari Shidama. The Lebesgue monotone convergence theorem.

*Formalized Mathematics*, 16(2):167-175, 2008. doi:10.2478/v10037-008-0023-1. [Crossref][11] Andrzej Kondracki. Basic properties of rational numbers.

*Formalized Mathematics*, 1(5): 841-845, 1990.[12] Jarosław Kotowicz. Convergent sequences and the limit of sequences.

*Formalized Mathematics*, 1(2):273-275, 1990.[13] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences.

*Formalized Mathematics*, 6(2):265-268, 1997.[14] Jan Popiołek. Some properties of functions modul and signum.

*Formalized Mathematics*, 1(2):263-264, 1990.[15] Andrzej Trybulec. Binary operations applied to functions.

*Formalized Mathematics*, 1 (2):329-334, 1990.[16] Michał J. Trybulec. Integers.

*Formalized Mathematics*, 1(3):501-505, 1990.[17] Zinaida Trybulec. Properties of subsets.

*Formalized Mathematics*, 1(1):67-71, 1990.[18] Edmund Woronowicz. Relations and their basic properties.

*Formalized Mathematics*, 1 (1):73-83, 1990.

Please log in or register to comment.

Log inRegisterHave you read our house rules for communicating on De Gruyter Online?

Published in Print: 2013-10-01Citation Information:Formalized Mathematics. Volume 21, Issue 3, Pages 163–170, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0018, October 2013This content is open access.