Partial Functions from a Domain to the Set of Real Numbers

Jaroslaw Kotowicz

Warsaw University, Bialystok

Supported by RPBP.III-24.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.

MML Identifier: RFUNCT_1

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.