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.

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.

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.

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

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

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

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

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.

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?

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.

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

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.

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.

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

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

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.

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

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

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

Imagine being the first one being killed on any of these tracks.

The probability of that is...?

Mathematicians tell me, please, because my mind is breaking.

I masturbate until I forget about the decision I have to make and then put off cleaning my apartment until I finally just run out, randomly pull the lever, and never think of the consequences again.

Of course by that point everyone has already starved to death which is the worst possible outcome.

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

This hypothetical post is a thought crime!

like the infinite monkeys with typewritters, universal limits to the rescue. Trolley's are slow. Each bump makes them slower. Some of the people in the discrete line will have long lives until an excruciatingly painful death from dehydration.

Hold the lever halfway so the trolley picks both rails at the same time, to ensure highest possible kill comboq

Bottom. Train will stall/derail faster.

Like everything else in this holographic universe we live in, I’d just close my eyes and believe the bodies I’m trampling are imaginary.

either way infinite people die, just not getting involved

What about a time loop where only one person dies, but infinite times?

Okay, so what’s the point of “proving” that there some “infinities” are “bigger” than others? What’s the practical application here? Because an infinite hotel with an infinite number of guests is physically impossible, so I don’t see the point.