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.III-24.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.

MML Identifier: LIMFUNC1

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.
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[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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