Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Convergent Real Sequences.
Upper and Lower Bound of Sets of Real Numbers
-
Jaroslaw Kotowicz
-
Warsaw University, Bialystok
-
Supported by RPBP.III-24.C8.
Summary.
-
The article contains theorems about convergent sequences and the limit
of sequences occurring in [5] such as
Bolzano-Weierstrass theorem, Cauchy theorem and others.
Bounded sets of real numbers and lower and upper bound
of subset of real numbers are defined.
MML Identifier:
SEQ_4
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[12]
[2]
[11]
[4]
[13]
[7]
[5]
[1]
[3]
[6]
[8]
[10]
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]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
- [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.
On the sets inhabited by numbers.
Journal of Formalized Mathematics,
15, 2003.
- [11]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received November 23, 1989
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