Volume 11, 1999

University of Bialystok

Copyright (c) 1999 Association of Mizar Users

**Richard Krueger**- University of Alberta, Edmonton
**Piotr Rudnicki**- University of Alberta, Edmonton
**Paul Shelley**- University of Alberta, Edmonton

- The widely used textbook by Brassard and Bratley [4] includes a chapter devoted to asymptotic notation (Chapter 3, pp. 79-97). We have attempted to test how suitable the current version of Mizar is for recording this type of material in its entirety. This article is a follow-up to [13] in which we introduced the basic notions and general theory. This article presents a Mizar formalization of examples and solutions to problems from Chapter 3 of [4] (some of the examples and solved problems are also in [13]). Not all problems have been solved as some required solutions not amenable for formalization.

This work has been supported by NSERC Grant OGP9207.

- Examples from the Text
- Problem 3.1
- Problem 3.5
- Problem 3.6
- Problem 3.7
- Problem 3.8
- Problem 3.11
- Problem 3.19
- Problem 3.21
- Problem 3.22
- Problem 3.23
- Problem 3.24
- Problem 3.26
- Problem 3.28
- Problem 3.30
- Problem 3.31
- Problem 3.34
- Problem 3.35
- Addition
- Potentatially Useful

- [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 and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [4] Gilles Brassard and Paul Bratley. \em Fundamentals of Algorithmics. Prentice Hall, 1996.
- [5]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [6]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [8]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
*Journal of Formalized Mathematics*, 1, 1989. - [11]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
*Journal of Formalized Mathematics*, 1, 1989. - [12]
Elzbieta Kraszewska and Jan Popiolek.
Series in Banach and Hilbert spaces.
*Journal of Formalized Mathematics*, 4, 1992. - [13]
Richard Krueger, Piotr Rudnicki, and Paul Shelley.
Asymptotic notation. Part I: Theory.
*Journal of Formalized Mathematics*, 11, 1999. - [14]
Rafal Kwiatek.
Factorial and Newton coefficients.
*Journal of Formalized Mathematics*, 2, 1990. - [15]
Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto.
Preliminaries to circuits, I.
*Journal of Formalized Mathematics*, 6, 1994. - [16]
Konrad Raczkowski and Andrzej Nedzusiak.
Real exponents and logarithms.
*Journal of Formalized Mathematics*, 2, 1990. - [17]
Konrad Raczkowski and Andrzej Nedzusiak.
Series.
*Journal of Formalized Mathematics*, 3, 1991. - [18]
Andrzej Trybulec.
Domains and their Cartesian products.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [20]
Andrzej Trybulec.
Function domains and Fr\aenkel operator.
*Journal of Formalized Mathematics*, 2, 1990. - [21]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [22]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Michal J. Trybulec.
Integers.
*Journal of Formalized Mathematics*, 2, 1990. - [24]
Wojciech A. Trybulec.
Pigeon hole principle.
*Journal of Formalized Mathematics*, 2, 1990. - [25]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [26]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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