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It is traditionally assumed that Zipf's law implies the power-law growth ofthe number of different elements with the total number of elements in a system- the so-called Heaps' law. We show that a careful definition of Zipf's lawleads to the violation of Heaps' law in random systems, and obtain alternativegrowth curves. These curves fulfill universal data collapses that only dependon the value of the Zipf's exponent. We observe that real books behave verymuch in the same way as random systems, despite the presence of burstiness inword occurrence. We advance an explanation for this unexpected correspondence.

Log-log Convexity of Type-Token Growth in Zipf's Systems