(a) Prove that f O(f) for all f: Z+ R. (b) Let f, g: Z+ ...
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(b) Let f, g: Z+ → R. If f ∈ O (g) and g ∈ 0(f), prove that 0(f) = 0(g). That is, prove that for all h: Z+ R, if h is dominated by f, then h is dominated by g, and conversely.
(c) If f, g: Z+ → R, prove that if 0(f) = 0(g), then f ∈ 0(g) and g ∈ O(f).
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Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
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