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

The Limit of a Composition of Real Functions


Jaroslaw Kotowicz
Warsaw University, Bialystok
Supported by RPBP.III-24.C8.

Summary.

The theorem on the proper and improper limit of a composition of real functions at a point, at infinity and one-side limits at a point are presented.

MML Identifier: LIMFUNC4

The terminology and notation used in this paper have been introduced in the following articles [9] [10] [2] [3] [8] [11] [1] [7] [5] [6] [4]

Contents (PDF format)

Bibliography

[1] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[2] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[4] Jaroslaw Kotowicz. The limit of a real function at a point. Journal of Formalized Mathematics, 2, 1990.
[5] Jaroslaw Kotowicz. The limit of a real function at infinity. Journal of Formalized Mathematics, 2, 1990.
[6] Jaroslaw Kotowicz. The one-side limits of a real function at a point. Journal of Formalized Mathematics, 2, 1990.
[7] Jaroslaw Kotowicz. Properties of real functions. Journal of Formalized Mathematics, 2, 1990.
[8] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.
[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[10] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[11] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received September 5, 1990


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