<< Zipf's Law says that the probability of the n'th most popular thingy is proportional to 1/n. Clearly this probability exists only if the universe of thingy's is finite.

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Actually Zipf's law applies to the commest *words* used, and assuming we're looking at N of them gives the k'th one a probability of (1/k) / (sum{j=1 to N} (1/j)), so it's normalized to 1. People have looked at a generalized Zipf's law, which allows a fixed exponent where you replace all the 1/C 's with 1/C^t 's -- which gives a good fit for things other than words with s <> 1. --Dan