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what if the number of people on the tracks is “infinite in both directions”? eg the trolley “starts at” -∞?
That's still the same size of infinity. Infinities are strange. But you can rearrange -∞ to ∞ to be the same size as 0 to ∞. You can do this by moving the negative numbers alongside their positive counterpart, like so:
0, 1, -1, 2, -2, 3, -3, etc.
This infinity is still a countable infinity, same as
0, 1, 2, 3, etc.
So it makes no difference whether you start at 0 or -∞
very true that infinities are strange. while starting at -∞ would not affect the cardinality, it would change the scenario.
we can think about starting at -∞ as counting the trolleys position using the integers, and we can think about starting at 0 as using the natural number to count the trolleys position. for example, the integer n would correspond to the trolley being on top of the n-th person. here we assume the trolley is moving to the right so the position increases as time passes. (if we change the setup so the trolley moves to the left, then it is possible that the trolley kills everyone in the second original setup but not the modified version.)
in the original setup, regardless of the trolleys position, the trolley would have killed finitely many people. (for any integer n, there are only finitely many nonnegative integers less than n). in the modified setup however, at any position, the trolley would have killed infinitely many people. (for any integer n, there are infinitely many integers less than n.) it’s a subtle difference but it does impact the scenario.
ChatGPT?
no i just have a decent background in pure math
Your post kinda reads like a chatgpt response with a few human touches added
maybe it’s the autism
Fair enough
yeah, but if it starts at -inf and I start at 0 then I don't have to look at the horrible things I'm allowing to happen
Also Think of the consequences of suddenly adding infinite people to the population
yeah that may cause a few problems. there would also need to be an infinite amount of trolley track which may pose some infrastructure challenges