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infinite mathematicians enter a bar. the first orders a pint of beer, the second orders half a pint. the third orders a quarter pint, and the bartender cuts them off there and just pours them two pints

after a time the mathematicians indicate they're ready for another round. as before, the first one orders a pint and the second orders a half. when the third orders a third of a pint the bartender says "actually i think you've all had enough for tonight"

infinite mathematicians are in a bar, nursing epsilons of beer from a previous order and getting a bit mischievous. catching the bartender's attention, the first orders a pint. the second orders two pints, the third three pints and so on. after a while the exasperated bartender pours a twelfth of a pint out of the mathematicians' glasses, at which point a brawl breaks out

@typhlosion A great many sequences start in those ways. How does the bartender know after only three terms that the mathematicians are using those specific sequences?

Related: I wonder if 1 + 1/2 + 1/3 + 1/6 + 1/11 converges, with the denominator of each term equal to the sum of the previous three denominators.

Related: is there any scholarly work on the behavior of Fibonacci-like sequences where you add the previous n>2 numbers?

@typhlosion and the bartender learned that they did not have infinite patience

@typhlosion I think the tribonacci numbers converge. My pen-and-paper math suggests the sum is close to 2.2

@typhlosion "epsilons of" is an amazing descriptor and my inner mathematician is mad I hadn't heard it before now

@typhlosion the group's mood didn't improve when they finally got back to their hotel and had to keep moving rooms the whole night

explaining the joke 

@Efi the divergent series 1+2+3+4+... and the number -1/12 appear together in a couple of interesting contexts: en.wikipedia.org/wiki/1_%2B_2_

@typhlosion ... not to nitpick the joke, but he should only pour the twelfth of the pint out of the first mathematician's glass.

This won't stop the brawl, mind you, but it will be more accurate. ^v^

joke defense 

@orrery why? the first joke uses 1+1/2+1/4...=2 to establish that the lot of them asking in a convergent series means the lot of them get two pints altogether, to split as they first wanted. then the third joke, using 1+2+3...=-1/12 (controversially, hence the brawl), would imply that the lot of them would lose a total of a twelfth of a pint

joke defense 

@orrery further, since it's stated in the setup that there are *epsilons* of beer left in the glasses, it would probably take more than one glass worth of dregs to equal a twelfth of a pint

joke defense 

@typhlosion Somehow I came away with the reading of the third joke that you were implying that each mathematician needed to lose a twelfth of a pint, which is why I spoke up. I got the humor; I just misread what you typed.

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