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

Property of Complex Functions


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

Summary.

This article introduces properties of complex function, calculations of them, boundedness and constant.

MML Identifier: CFUNCT_1

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

Contents (PDF format)

  1. Definitions of Complex Functions
  2. Basic Properties of Operations
  3. Total Partial Functions from a Domain, to Complex
  4. Bounded and Constant Partial Functions from a Domain, to Complex

Bibliography

[1] Agnieszka Banachowicz and Anna Winnicka. Complex sequences. Journal of Formalized Mathematics, 5, 1993.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. The complex numbers. Journal of Formalized Mathematics, 2, 1990.
[6] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[7] Jaroslaw Kotowicz. Partial functions from a domain to a domain. Journal of Formalized Mathematics, 2, 1990.
[8] Jaroslaw Kotowicz. Partial functions from a domain to the set of real numbers. Journal of Formalized Mathematics, 2, 1990.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[11] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[12] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[13] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received December 7, 1999


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