Talk:Heaps' law

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Divergence[edit]

I think with "Where VR is the subset of the vocabulary V represented by the instance text of size n" the author wanted to say "Where VR is the cardinality of the subset of the vocabulary V represented by the instance text of size n", because a subset is not a number. However, the size of the subset diverges (i.e. becomes arbitrarily large) as n goes towards infinity. That would only make sense if the vocabulary would also be of infinite size. (just as a sidenote: I would have expected the fraction of the vocabulary not covered by the text to decrease exponentially when looking at larger and larger documents). Icek (talk) 19:02, 29 September 2009 (UTC)

Vocabulary size is infinite according to generative grammar, see e.g. Mark Aronoff "Word formation in generative Grammar" MIT Press 1985, Andras Kornai "How many words are there?" Glottometrics 2002/4 61-86 88.132.28.96 (talk) 20:33, 17 March 2012 (UTC)