Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
The Limit of a Real Function at Infinity

Jaroslaw Kotowicz

Warsaw University, Bialystok

Supported by RPBP.III24.C8.
Summary.

We introduced the halflines ({\it open} and {\it closed}),
real sequences divergent to infinity ({\it plus} and {\it minus}) and
the proper and improper limit of a real function at infinty.
We prove basic properties of halflines, sequences divergent
to infinity and the limit of function at infinity.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[14]
[1]
[12]
[2]
[9]
[5]
[3]
[4]
[8]
[15]
[13]
[6]
[10]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Jaroslaw Kotowicz.
Partial functions from a domain to the set of real numbers.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Jaroslaw Kotowicz.
Properties of real functions.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Andrzej Nedzusiak.
$\sigma$fields and probability.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Konrad Raczkowski and Pawel Sadowski.
Topological properties of subsets in real numbers.
Journal of Formalized Mathematics,
2, 1990.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received August 20, 1990
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