# Double Sequences and Limits

Noboru Endou; Hiroyuki Okazaki; Yasunari Shidama

Formalized Mathematics (2013)

- Volume: 21, Issue: 3, page 163-170
- ISSN: 1426-2630

## Access Full Article

top## Abstract

top## How to cite

topNoboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. "Double Sequences and Limits." Formalized Mathematics 21.3 (2013): 163-170. <http://eudml.org/doc/266553>.

@article{NoboruEndou2013,

abstract = {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.},

author = {Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama},

journal = {Formalized Mathematics},

keywords = {formalization of basic metric space; limits of double sequences},

language = {eng},

number = {3},

pages = {163-170},

title = {Double Sequences and Limits},

url = {http://eudml.org/doc/266553},

volume = {21},

year = {2013},

}

TY - JOUR

AU - Noboru Endou

AU - Hiroyuki Okazaki

AU - Yasunari Shidama

TI - Double Sequences and Limits

JO - Formalized Mathematics

PY - 2013

VL - 21

IS - 3

SP - 163

EP - 170

AB - 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.

LA - eng

KW - formalization of basic metric space; limits of double sequences

UR - http://eudml.org/doc/266553

ER -

## References

top- [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
- [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] Zbl1321.46022
- [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.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.