In the top one you will never actually kill an infinite number of people, just approach it linearly. The bottom one will kill an infinite amount of people in finite time.

Edit: assuming constant speed of the train.

Bottom.

Killing one person for every real number implies there’s a way to count all real numbers one by one. This is a contradiction, because real numbers are uncountable. By principle of explosion, I’m Superman, which means I can stop the train by my super powers. QED

Use the fact that a set of people corresponding to the real numbers are laying in a single line to prove that the real numbers are countable, thus throwing the mathematics community into chaos, and using this as a distraction to sabotage the trolley and save everybody.

First, I start moving people to hotel rooms...

I pull the lever, if the cart goes over the real numbers it will instantly kill an infinite amount of people and continue killing an infinite amount of people for every moment for the rest of existence.

If I pull the lever a finite amount of people will die instantly and slowly over time tending twords infinity but due to the linear nature of movement it would never actually reach Infinity even if there are an infinite number of people tied to the track a finite amount is all that could ever die.

Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.

The first one, because people will die at a slower rate.

The second one, because the density will cause the trolley to slow down sooner, versus the first one where it will be able to pick up speed again between each person. Also, more time to save people down the rail with my handy rope cutting knife.

I ignore the question and go to the IT and maintenance teams to put a series of blocks, physical and communication-system-based, between the maths and philosophy departments. Attempts to breach containment will be met with deadly force.

I think it was numberphile, or maybe vsauce, who did a video on infinities. It was really interesting. I learnt a lot, then forgot it all.

The second one. It'll be a bit rough, but overall should be a smoother ride for the occupants.

The top one, because time is still a factor.

Sure, infinite people will die either way, but that is only after infinite time.

Is there a way to take both routes?

I mean, the bottom. The trolley simply would stop, get gunked up by all the guts and the sheer amount of bodies so close together. Checkmate tolley.

Considering that there's a small but non zero chance of surviving getting ran over by a train some of them are gonna survive this and since there are infinite people that will result in infinite train-proof people spawning machine

you know, I'm not sure you can have an uncountably infinite number of people. so whatever that abomination is I'll send the trolley down its way. it's probably an SCP.

In the top case has it been arbitrarily decided to include space in between the would-be victims? Or is the top a like number line comparison to the bottom? Because if thats the case it becomes relevant if there is one body for every real number unit of distance. (One body at 0.1 meter, and at 0.01 meter, at 0.001, etc)

If so then there's an infinite amount of victims on the first planck length of the bottom track. An infinite number of victims would contain every possible victim. Every single possible person on the first plank length. So on the next planck length would be every possible person again.

Which would mean that the bottom track is actually choosing a universe of perpetual endless suffering and death for every single possible person. The top track would eventually cause infinite suffering but it would take infinite time to get there. The bottom track starts at infinite suffering and extends infinitely in this manner. Every possible version of every possible person dying, forever.

Bottom. No matter what your "real" number assignation in the queue is, theres an infinite number of people before the train gets to you. Therefore every single person will live a full life before the train reaches them.

Bottom. Greater probability that it gets stuck in the corpses.

Top case is not the smallest infinite; going for prime number would save a lot of time for a lot of people before they die

3. I lay some extra track so the train runs over the perverts that come up with these "dilemmas" instead. Problem solved. 👍

Good to know there are roughly 6 real numbers for every integer

Getting killed by a train is apparently just an inevitability in this universe. Either choice is just the grand conductors plan.

Doesn't matter, there are not enough people to try this anyway

Some infinities are bigger than other infinities

Is this actually true?

Many eons ago when I was in college, I worked with a guy who was a math major. He was a bit of a show boat know it all and I honestly think he believed that he was never wrong. This post reminded me of him because he and I had a debate / discussion on this topic and I came away from that feeling like he he was right and I was too dumb to understand why he was right.

He was arguing that if two sets are both infinite, then they are the same size (i.e. infinity, infinite). From a strictly logical perspective, it seemed to me that even if two sets were infinite, it seems like one could still be larger than the other (or maybe the better way of phrasing it was that one grew faster than the other) and I used the example of even integers versus all integers. He called me an idiot and honestly, I've always just assumed I was wrong -- he was a math major at a mid-ranked state school after all, how could he be wrong?

Thoughts?

I thought that the correct answer to these was making a loop on the right, merging the lines.