I actually agree with your example. The point is that nobody should care whether one interprets the looping variable (and underlying sum) as mutation or as shorthand for a mutationless expression. It's pretentious and counterproductive to call one interpretation mathematics and the other not.
Right - my point was more in the context of the idea that to correctly translate that mathematical concept to code you are doing it wrong if you use mutation. If a mathematical algorithm you're implementing contains a summation, you're not fundamentally misrepresenting the underlying mathematical purity if you implement it as a for loop with an accumulator.
