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Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Can you help me with writing this proof for Big-Oh?

3. Asymptotic notation. For each part of this question, you may (but are not required to) use any of the following facts. • Fact 1: Vn E Z, n < 2" • Fact 2: Vx, y E R†, x < y log2 (x) < log2(y) • Fact 3: Vx, y E R, x < y + 2" < 2º You may NOT use any of the facts from pages 92-95 in the Course Notes. Your proofs must depend only on elementary properties of logarithms and exponential functions, together with the facts above. (a) Let k be a positive real number. Prove or disprove that log2(k+n) E O(log2 n).
Transcribed Image Text:3. Asymptotic notation. For each part of this question, you may (but are not required to) use any of the following facts. • Fact 1: Vn E Z, n < 2" • Fact 2: Vx, y E R†, x < y log2 (x) < log2(y) • Fact 3: Vx, y E R, x < y + 2" < 2º You may NOT use any of the facts from pages 92-95 in the Course Notes. Your proofs must depend only on elementary properties of logarithms and exponential functions, together with the facts above. (a) Let k be a positive real number. Prove or disprove that log2(k+n) E O(log2 n).
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