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.
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