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.
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]

Definitions of Complex Functions

Basic Properties of Operations

Total Partial Functions from a Domain, to Complex

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
[
Download a postscript version,
MML identifier index,
Mizar home page]