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I understand that $f(n) \leq Ng(n)$ and $g(n) \leq Nh(n)$ so obviously $f(n) \leq Nh(n)$, but how would one go about proving this using proper semantics (using big $O$ notation)?

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    "obviously $f(n) \leq Nh(n)$": That's not quite right.2011-12-11

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