Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Basic Properties of Rational Numbers


Andrzej Kondracki
Warsaw University
Supported by RPBP.III-24.C1.

Summary.

A definition of rational numbers and some basic properties of them. Operations of addition, subtraction, multiplication are redefined for rational numbers. Functors numerator (num $p$) and denominator (den $p$) ($p$ is rational) are defined and some properties of them are presented. Density of rational numbers is also given.

MML Identifier: RAT_1

The terminology and notation used in this paper have been introduced in the following articles [7] [4] [10] [2] [3] [8] [5] [1] [6] [9]

Contents (PDF format)

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[6] Jan Popiolek. Some properties of functions modul and signum. Journal of Formalized Mathematics, 1, 1989.
[7] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[8] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[9] Michal J. Trybulec. Integers. Journal of Formalized Mathematics, 2, 1990.
[10] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

Received July 10, 1990


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