The finite analogue come from the fact that infinity minus infinity is undefined, and can be anything from “still infinity” (like if you had infinity people and then only sent away the even numbered ones) to any number you choose, to negative infinity. In a finite problem, the answer becomes well-defined, but there are multiple possible answers.
Consider the converse: Is there a way to arrange the days and people such that it is better to start in hell? Trivially, it seems like the simple solution is that way, since each person leaves hell after a finite number of days and then spends infinity days in heaven, but I lack the concept which allows me to find the amount of time the average person spends in hell.
Conclusions that involve infinity cannot generally be generalized to any finite solution; this seems like a ‘each monkey now has two bananas’ moment.
The finite analogue come from the fact that infinity minus infinity is undefined, and can be anything from “still infinity” (like if you had infinity people and then only sent away the even numbered ones) to any number you choose, to negative infinity. In a finite problem, the answer becomes well-defined, but there are multiple possible answers.
Yeah, that’s the point.
Consider the converse: Is there a way to arrange the days and people such that it is better to start in hell? Trivially, it seems like the simple solution is that way, since each person leaves hell after a finite number of days and then spends infinity days in heaven, but I lack the concept which allows me to find the amount of time the average person spends in hell.
By the way, are you talking about this meme, or is there another problem with monkeys and bananas?
I was talking about the math that spawned that meme, yes.