Welcome to infinity, where the limits (in the mathematical sense) are fake and nothing makes sense. You can both prove that the number of dead people is the same in all cases and that at any given point the leftmost track has killed five times as many people as the rightmost track.
Nooo it all makes sense as long as you follow the rules :)
Next let’s consider the following tracks:
----- ... -|----
/
o ---||| ... |||---
So the top track has 1 victim, the bottom has infinitely many. Now repeat them both infinitely many times. Do the two tracks have the same number of victims? Well in one way yes (both are infinite) but in another way no. Because the first victim in the first repeat of the bottom track had infinitely many victims before them, whereas there is no victim in the repeated top track that had infinitely many victims before them.
In mathematical terms, the cardinality of the victims is the same (there are “as many”) but the order type is not. (This is unlike OP’s example, where after infinitely many repetitions, the order type is the same)
Welcome to infinity, where the limits (in the mathematical sense) are fake and nothing makes sense. You can both prove that the number of dead people is the same in all cases and that at any given point the leftmost track has killed five times as many people as the rightmost track.
This is why I’m a finitist.
Nooo it all makes sense as long as you follow the rules :)
Next let’s consider the following tracks:
----- ... -|---- / o ---||| ... |||---So the top track has 1 victim, the bottom has infinitely many. Now repeat them both infinitely many times. Do the two tracks have the same number of victims? Well in one way yes (both are infinite) but in another way no. Because the first victim in the first repeat of the bottom track had infinitely many victims before them, whereas there is no victim in the repeated top track that had infinitely many victims before them.
In mathematical terms, the cardinality of the victims is the same (there are “as many”) but the order type is not. (This is unlike OP’s example, where after infinitely many repetitions, the order type is the same)