Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997
Association of Mizar Users
Convergence and the Limit of Complex Sequences. Series

Yasunari Shidama

Shinshu University, Nagano

Artur Kornilowicz

Warsaw University, Bialystok
The terminology and notation used in this paper have been
introduced in the following articles
[16]
[3]
[15]
[6]
[7]
[17]
[4]
[10]
[8]
[2]
[9]
[12]
[14]
[5]
[1]
[11]
[13]

Preliminaries

The Operations on Complex Sequences

Convergence of Complex Sequences

Summable and Absolutely Summable Complex Sequences
Bibliography
 [1]
Agnieszka Banachowicz and Anna Winnicka.
Complex sequences.
Journal of Formalized Mathematics,
5, 1993.
 [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
The complex numbers.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Library Committee.
Introduction to arithmetic.
Journal of Formalized Mathematics,
Addenda, 2003.
 [7]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Adam Naumowicz.
Conjugate sequences, bounded complex sequences and convergent complex sequences.
Journal of Formalized Mathematics,
8, 1996.
 [12]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Konrad Raczkowski and Andrzej Nedzusiak.
Real exponents and logarithms.
Journal of Formalized Mathematics,
2, 1990.
 [14]
Konrad Raczkowski and Andrzej Nedzusiak.
Series.
Journal of Formalized Mathematics,
3, 1991.
 [15]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [16]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [17]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 25, 1997
[
Download a postscript version,
MML identifier index,
Mizar home page]