:Er, what? 
 :> the assumption that the cost of calculating a hash and performing a comparison is comparable asymptotically, which is not the case when n goes to infinity 
 :The complexity of calculating the hash is assumed to be constant, just like greater/less comparisons in a tree lookup aren't factored into the O() complexity. That's a fair assumption given constant-length keys. 
 :> Indeed, if you have a set of n elements, you need at least log(n) bits to represent them 
 :This applies just as well to a binary tree structure that needs to store left/right pointers, pointer size needs to be at least log(n). So by your argument its complexity should be O(log(log n))? 
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