This is completely wrong. Big O has nothing to do with algorithms. Big O notation can be used for any mathematical function from an ordered set to another order

This is completely wrong. Big O has nothing to do with algorithms. Big O notation can be used for any mathematical function from an ordered set to another ordered set, including average runtime of an algorithm as a function of data size, worst-case runtime of an algorithm as a function of data size, guaranteed amortized runtime of an algorithm as a function of data size, or anything else (including things with nothing to do with computation -- it's perfectly reasonable to say things like x^2 + 5x + 2 is O(x^2) and just be talking about pure math with no reference to algorithms). If someone asked "what is the runtime of quicksort in big O terms", it is ambiguous whether the answer is O(n^2) or O(n*log(n)) , since it's not clear which function you're talking about.