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.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

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

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