> There are theoretical limits to the upper bound of problem size. Big O is defined as what happens as the size of the input approaches infinity. You cannot ta

> There are theoretical limits to the upper bound of problem size. Big O is defined as what happens as the size of the input approaches infinity. You cannot take a O(log n) algorithm and say it is effectively O(1), that is not what big O means. If anything, you are arguing for why big O notation is a bad measure for the efficiency of an algorithm, not why you can call a O(log n) algorithm O(1).