Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Partial Functions from a Domain to the Set of Real Numbers

Jaroslaw Kotowicz

Warsaw University, Bialystok

Supported by RPBP.III24.C8.
Summary.

Basic operations in the set of partial
functions which map a domain to the set of all real numbers are introduced.
They include adition, subtraction, multiplication, division,
multipication by a real number and also module.
Main properties of these operations are proved. A definition of the partial
function bounded on a set (bounded below and bounded above) is presented.
There are theorems showing the laws of conservation of totality and
boundedness for operations of partial functions.
The characteristic function of a subset of a domain as
a partial function is redefined and a few properties are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[11]
[1]
[10]
[5]
[3]
[2]
[8]
[12]
[4]
[7]
[6]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Basic functions and operations on functions.
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]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [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]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [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]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received May 27, 1990
[
Download a postscript version,
MML identifier index,
Mizar home page]