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Entropy of an infinite sequence?

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up vote 0 down vote favorite 1 Does an infinite sequence always have finite entropy? For example, doesn't $a_n=n$ , the sequence of non-negative integers, have very low entropy? It feels like all "well-defined" sequences ought to have low entropy because there's very little surprise about the next element. sequences-and-series information-theory entropy share | cite | improve this question asked Nov 18 at 16:21 Matt Thomas 166 6 1 ...