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by paraknight 1973 days ago
Can you explain?
3 comments

1 + 2 + 3 + ... = -1/12 total beers

-1/12 beers * $3 / beer = -$0.25

negative -> pay them for taking the beer

The -1/12 result is pretty widely known, but not particularly true. It's called "analytic continuation." There's a nonrigorous proof that's accessible at a highschool level - see [here](https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...)

Delightfully, this comes up in string theory, in computing the dimensionality of spacetime.

It's referencing a theorem from string theory, as discussed in this Numberphile video: https://www.youtube.com/watch?v=w-I6XTVZXww

The catch is that this isn't valid in what we consider standard mathematics, and you can find many discussions of this online, but this one is fairly short and straightforward: http://curiouscheetah.com/BlogMath/infinity-and-string-theor...

The sum of all positive integers can be somewhat described as negative one twelfth: https://www.youtube.com/watch?v=E-d9mgo8FGk