There is more than one way to do infinite sums. Such paradoxical results seem to violate the laws of arithmetic, but actually point to new kinds of arithmetics, with alternate laws. In this case, we see what happens when an alternating sum of 1s and minus 1s is assigned the plausible value of 1/2. This result comes along with that for free. All thats involved is a shifting concept of infinite sum. It isnt written in stone that the concept taught in elementary calculus classes is the only permissible concept.
Posted on: Sat, 18 Jan 2014 08:01:25 +0000