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Maybe a newbie question, but why when we analyze algorithms do we focus on asymptotics? It seems to me the performance of algorithms on finite input sizes (after all, problems are rarely infinitely large) should be as important or more so than when they tend to infinity. Do things simply become too complicated and nuanced if we don't allow $n \to \infty$?

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merged by Gilles 'SO- stop being evil' Jan 4 '16 at 18:08

This question was merged with Explaining the relevance of asymptotic complexity of algorithms to practice of designing algorithms because it is an exact duplicate of that question.