This argument comes up all the time, and the answer is that big-O notation is very general, and only makes sense relative to a particular computation model. For

This argument comes up all the time, and the answer is that big-O notation is very general, and only makes sense relative to a particular computation model. For example, you may describe a sorting algorithm's complexity by counting the number of comparisons, abstracting away details like memory caching or arbitrarily-sized elements. So it's perfectly reasonable for the original author to call arithmeticSum constant time, assuming that the numbers are bounded, and it's also perfectly reasonable for other researchers to say that multiplication is O(n log n), without that assumption.