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: Saying a sorting algorithm is O(nlogn) allows the execution with particular input to be less than nlogn; bubble sort taking n comparisons is not a surprise; it does not contradict the bound.
: Some algorithms are strictly Θ(nlogn). Heapsort goes through all the motions no matter what. But that doesn't mean all sorting has such a lower bound.
: Saying a sorting algorithm is Ω(nlogn) says it can never do better than nlogn. Bubblesort does better once in a while.
: Throwing in "average case" or "worst case" muddies an order statistic.
: Speaking of Ω() in the context of "worst case" is really speaking in terms of an upper bound (the worst case) rather than a lower bound.
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