It is traditionally assumed that Zipf's law implies the power-law growth of
the 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 law
leads to the violation of Heaps' law in random systems, and obtain alternative
growth curves. These curves fulfill universal data collapses that only depend
on the value of the Zipf's exponent. We observe that real books behave very
much in the same way as random systems, despite the presence of burstiness in
word occurrence. We advance an explanation for this unexpected correspondence