Memes

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.