> i.e. to store distinct N=2^32 elements, you need N log(N) = 2^32 * 32 bits, but to store N=2^64 elements, you need 2^64 * 64 bits N is the number of bits, no

> i.e. to store distinct N=2^32 elements, you need N log(N) = 2^32 * 32 bits, but to store N=2^64 elements, you need 2^64 * 64 bits N is the number of bits, not the number of elements, so no. It is helpful to use N=# of elements, since the elements are often fixed/limited size. If elements aren't a fixed size, it's necessary to drop down to # of bits.