Białystok Asymptotic Notation . Part I : Theory 1
نویسندگان
چکیده
The widely used textbook by Brassard and Bratley [3] 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. A more detailed report on this experiment will be available separately. This article presents the development of notions and a follow-up article [11] includes examples and solutions to problems. The preliminaries introduce a number of properties of real sequences, some operations on real sequences, and a characterization of convergence. The remaining sections in this article correspond to sections of Chapter 3 of [3]. Section 2 defines the O notation and proves the threshold, maximum, and limit rules. Section 3 introduces the Ω and Θ notations and their analogous rules. Conditional asymptotic notation is defined in Section 4 where smooth functions are also discussed. Section 5 defines some operations on asymptotic notation (we have decided not to introduce the asymptotic notation for functions of several variables as it is a straightforward generalization of notions for unary functions).
منابع مشابه
The Nagata - Smirnov Theorem . Part II 1 Karol Pa̧k University of Białystok
The terminology and notation used in this paper have been introduced in the following articles: [9], [27], [28], [32], [20], [5], [12], [8], [21], [15], [2], [17], [14], [18], [19], [6], [10], [11], [24], [23], [4], [33], [1], [3], [25], [16], [26], [7], [13], [29], [31], [34], [30], and [22]. For simplicity, we adopt the following convention: i, k, m, n denote natural numbers, r, s denote real...
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