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.III24.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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