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.
@article{bwmeta1.element.doi-10_2478_forma-2013-0018, author = {Noboru Endou and Hiroyuki Okazaki and Yasunari Shidama}, title = {Double Sequences and Limits}, journal = {Formalized Mathematics}, volume = {21}, year = {2013}, pages = {163-170}, zbl = {1298.40003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0018} }
Noboru Endou; Hiroyuki Okazaki; Yasunari Shidama. Double Sequences and Limits. Formalized Mathematics, Tome 21 (2013) pp. 163-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0018/
[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858
[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] | Zbl 1321.46022
[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.