I take the square root of all the negative real numbers and kill in an entirely new dimension.

I remember seeing a science show on PBS where the presenter explained how there are different infinities by using set theory and the integers/reals. That was mind-blowing at the time.

I reject the premise since there will only ever exist a finite number of people. They will all die. One day the last human will die.

I would pull the lever and then steal a bus and knock the trolley off of the track, killing the least amount of people possible.

sort them so you kill one person first, then 2, then 3, then 4...

there are more real numbers than integers though

"smallest"?

You've misunderstood "some infinities are bigger than others." Both of these infinities are the same size. You can show this since each person on the bottom track can be assigned a person from the top track at 1 to 1 ratio. An example of infinities that are different sizes are all whole numbers and all decimal numbers. You cannot assign a whole number to every decimal number.

Matt parker does a good video on this. I can't remember the exact title but if you search "is infinite $20 notes worth more than infinite $1 notes" you should find it.