Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

Property of Complex Sequence and Continuity of Complex Function


Takashi Mitsuishi
Shinshu University, Nagano
Katsumi Wasaki
Shinshu University, Nagano
Yasunari Shidama
Shinshu University, Nagano

Summary.

This article introduces properties of complex sequence and continuity of complex function. The first section shows convergence of complex sequence and constant complex sequence. In the next section, definition of continuity of complex function and properties of continuous complex function are shown.

MML Identifier: CFCONT_1

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

Contents (PDF format)

  1. Complex Sequence
  2. Continuity of Complex Sequence

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] Czeslaw Bylinski. Functions and their basic properties. 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. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. The complex numbers. Journal of Formalized Mathematics, 2, 1990.
[7] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.
[8] Takashi Mitsuishi, Katsumi Wasaki, and Yasunari Shidama. Property of complex functions. Journal of Formalized Mathematics, 11, 1999.
[9] Adam Naumowicz. Conjugate sequences, bounded complex sequences and convergent complex sequences. Journal of Formalized Mathematics, 8, 1996.
[10] Yasunari Shidama and Artur Kornilowicz. Convergence and the limit of complex sequences. Series. Journal of Formalized Mathematics, 9, 1997.
[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[12] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[13] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[16] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received December 7, 1999

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