think of a set as an unordered list of unique items.
if you don’t sort the set, oeprations take linear time ⇒ o(n).
however, if you sort the set, finding an object can take log^n time.
if every step is divided by a constant factor, that's log(n).
tried implementing a merge-sort algorithm. failed in the first attempt, even though i understood it; but failed to translate it into code.