Only the real cardinallity must. The integer cardinallity could have them spaced out enough that they won’t collapse.
For you to do this trolley problem you’d need to be outside the real track black hole so the question becomes: do you let a trolley go into a black hole or do you switch it to an infinite track that kills an infinite number of people?
Edit: in which case the black hole must be infinitely far away and you don’t even know about it. So: do you pull the switch to cause a trolley to start killing a seemingly infinite number of people? Which based on the other replies in this thread the answer is a resounding “yes”
No. In any interval of the real numbers there’s an uncountable infinity of real numbers. No matter how much you stretch the track any neighborhood, no matter how small, will need an infinite number of people in it.
There being a person for every real number doesn’t mean there’s a person at every real point on the track. If it did, then there would be people inside of each other, and we can visually see that the people are laid down next to one another.
No. If you put them in order one after another you are not talking about the real numbers. There is no “next” real number and no possible way to visit them all one at a time like with the rationals.
Only the real cardinallity must. The integer cardinallity could have them spaced out enough that they won’t collapse.
For you to do this trolley problem you’d need to be outside the real track black hole so the question becomes: do you let a trolley go into a black hole or do you switch it to an infinite track that kills an infinite number of people?
Edit: in which case the black hole must be infinitely far away and you don’t even know about it. So: do you pull the switch to cause a trolley to start killing a seemingly infinite number of people? Which based on the other replies in this thread the answer is a resounding “yes”
Given infinite track, the reals could have enough space between them to avoid collapsing too
No. In any interval of the real numbers there’s an uncountable infinity of real numbers. No matter how much you stretch the track any neighborhood, no matter how small, will need an infinite number of people in it.
There being a person for every real number doesn’t mean there’s a person at every real point on the track. If it did, then there would be people inside of each other, and we can visually see that the people are laid down next to one another.
No. If you put them in order one after another you are not talking about the real numbers. There is no “next” real number and no possible way to visit them all one at a time like with the rationals.