Journal of Formalized Mathematics
Volume 5, 1993
University of Bialystok
Copyright (c) 1993 Association of Mizar Users

## Properties of Partial Functions from a Domain to the Set of Real Numbers

Jaroslaw Kotowicz
Warsaw University, Bialystok
Yuji Sakai
Shinshu University, Nagano

### Summary.

The article consists of two parts. In the first one we consider notion of nonnegative and nonpositive part of a real numbers. In the second we consider partial function from a domain to the set of real numbers (or more general to a domain). We define a few new operations for these functions and show connections between finite sequences of real numbers and functions which domain is finite. We introduce {\em integrations} for finite domain real valued functions.

#### MML Identifier: RFUNCT_3

The terminology and notation used in this paper have been introduced in the following articles [22] [26] [2] [23] [27] [5] [3] [4] [1] [12] [18] [20] [21] [8] [24] [28] [6] [7] [13] [16] [25] [10] [9] [19] [15] [14] [11] [17]

#### Contents (PDF format)

1. Nonnegative and Nonpositive Part of a Real Number
2. Properties of Real Function

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