I watched a video of numberphile in which they explain that how you can get Grandi's series sum as $1/2$ ( by Cesàro summation). Then they also give one example of flipping of bulb $1$ means turn on and $0$ means turn off and puts a question to the viewer,what do you think will happen at infinity will it be half turned on half turned off. So my question is : Isn't it all kinda big baloney act first of all there is no such thing as infinity it is not physically realizable and real numbers never end and doesn't the answer seem staring right at the face bulb will be going to toggle between on and off as you change the switch. I find the whole question pointless but my colleagues are telling me that I am acting as an orthodox and I am not allowing any scope of new ideas to grow.

  • $\begingroup$ You seem to be asking whether Cesàro summation is a valid procedure or not, and that isn't a physics question. You might be better asking on the Maths SE. $\endgroup$ – John Rennie May 4 '18 at 9:20
  • $\begingroup$ math.stackexchange.com/a/1404060/155436 $\endgroup$ – Count Iblis May 4 '18 at 9:20
  • $\begingroup$ No I am saying asking for physical interpretation of such thing is out of question in first place. I don't have any issue with whatever result the technique produce like $\Gamma(-1)=-1/12$ to provide you an example. $\endgroup$ – aitfel May 4 '18 at 9:24
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    $\begingroup$ Related: physics.stackexchange.com/q/19356/2451 , physics.stackexchange.com/q/26877/2451 and links therein. $\endgroup$ – Qmechanic May 4 '18 at 9:46
  • $\begingroup$ The correct interpretation is (in my opinion) that after a while you can only give the probability with which the lamp will be burning and this exactly the result of Grandi's series. Of course one could then wonder about the interpretation of the series leading to -1/12. $\endgroup$ – NDewolf May 4 '18 at 9:46