The Sum of All Natural Integers is -1/12

You read the Slate article too, I see.

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Pretty straight forward really

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Of course. Math is really easy when you bastardize it and don't follow the rules of infinite series.


The first series doesn't converge on any one number. You cannot take the average of it and call it a day. You can take the average of a similar alternating (signs) infinite series when it does appear to be converging on a number when you approach infinity (ie, each two new sum's difference as n--> infinity has less difference than the previous two. At that point, you may take an average. When you are constantly alternating between two sums without approaching anything, the function only had value for certain 'n;' and the series has no value.


ETA: mathematicians, please excuse my attempt to simplify the terms. And please add what I am missing, if I did not hit on it.

Silly.

I like the 1=0 one better. my calc prof did that first day and said "wait till we get to calculus"

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I think that since you're always in transition between the light on and the light off and as the speed at which you transition between on and off increases and the time of which it's either on or off shortens, it gets closer and closer to impossible to tell if the lights on or if the lights off. If this goes on for an infinite amount of time and what it actually looks like in the room is that the room will look dimly light, with a light intensity that's half way between on and off. Hence the 1/2 answer. ?

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From the comments (and explained later in the video).


I'm not a mathematician, but I had a problem with the way he just threw in those plus signs after he added the "1" before the brackets. Something seems fundamentally wrong doing that. Again, could be wrong.

Two wrongs don't make a right.

Not true