5 ms·
An infinite number of mathematicians walk into a bar, where a beer costs 3$. The first mathematician orders a beer. The second mathematician orders two beers.
by ulucs 6y ago
An infinite number of mathematicians walk into a bar, where a beer costs 3$.
The first mathematician orders a beer.
The second mathematician orders two beers.
The third mathematician orders three beers.
"Oh, I see where this is going" says the bartender and pays a quarter to the first mathematician. "This should cover your check, then."
- paraknight 6y agoCan you explain?
- duffmancd 6y agoThe sum of all positive integers can be somewhat described as negative one twelfth: https://www.youtube.com/watch?v=E-d9mgo8FGk https://www.youtube.com/watch?v=E-d9mgo8FGk
- 9000 6y agoIt's referencing a theorem from string theory, as discussed in this Numberphile video: https://www.youtube.com/watch?v=w-I6XTVZXww 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-theory/ http://curiouscheetah.com/BlogMath/infinity-and-string-theor...
- dmlerner 6y ago1 + 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%AF 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.
- smolder 6y agoIs this an antijoke or did I just need to know where it's going, like the bartender? Maybe the bartender is confused?
- evanb 6y agoThis joke relies on the listener knowing that the regularized sum of 1+2+3+... = -1/12.
- enriquto 6y agoThat's what makes it funny!
- Thorondor 6y agoThe joke is that the Ramanujan sum of 1 + 2 + 3 + 4 + ... is equal to -1/12, so the check should be $3 * -1/12 = minus one quarter. [0] [0]: https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B...
- smolder 6y agoThanks, that's a bit of math trivia I either forgot or never learned.