I wish to discuss the element uniqueness problem. First let's define the problem:Definition from wikipedia:In computational complexity theory, the element distinctness problem  or element uniqueness problem is the problem of determining whether  all the elements of a list are distinct.i am aware that this question has been asked before, however, I am confused about what lower bound actually means.Let's say we are given an arbitrary array of integers. We could simply use hashing to check for element uniqueness. Hashing works in amortized $O(1)$ time. Hence, shouldn't the lower bound of element uniqueness be $\Omega(n)$?Am I understanding lower bound wrongly? Does lower bound mean an asymptotic lower bound for general cases (i.e. we could have arrays of strings as well) or does it apply to all cases?
Why is the lower bound of element uniqueness in $\Omega(n\log n)$?
complexity theory;lower bounds
We assume the comparison model in the lower bound of the element uniqueness problem. That is, the key operations are to compare elements. In particular, hashing is not allowed.