this post was submitted on 02 Oct 2025
405 points (98.8% liked)
Science Memes
16932 readers
3236 users here now
Welcome to c/science_memes @ Mander.xyz!
A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.
Rules
- Don't throw mud. Behave like an intellectual and remember the human.
- Keep it rooted (on topic).
- No spam.
- Infographics welcome, get schooled.
This is a science community. We use the Dawkins definition of meme.
Research Committee
Other Mander Communities
Science and Research
Biology and Life Sciences
- !abiogenesis@mander.xyz
- !animal-behavior@mander.xyz
- !anthropology@mander.xyz
- !arachnology@mander.xyz
- !balconygardening@slrpnk.net
- !biodiversity@mander.xyz
- !biology@mander.xyz
- !biophysics@mander.xyz
- !botany@mander.xyz
- !ecology@mander.xyz
- !entomology@mander.xyz
- !fermentation@mander.xyz
- !herpetology@mander.xyz
- !houseplants@mander.xyz
- !medicine@mander.xyz
- !microscopy@mander.xyz
- !mycology@mander.xyz
- !nudibranchs@mander.xyz
- !nutrition@mander.xyz
- !palaeoecology@mander.xyz
- !palaeontology@mander.xyz
- !photosynthesis@mander.xyz
- !plantid@mander.xyz
- !plants@mander.xyz
- !reptiles and amphibians@mander.xyz
Physical Sciences
- !astronomy@mander.xyz
- !chemistry@mander.xyz
- !earthscience@mander.xyz
- !geography@mander.xyz
- !geospatial@mander.xyz
- !nuclear@mander.xyz
- !physics@mander.xyz
- !quantum-computing@mander.xyz
- !spectroscopy@mander.xyz
Humanities and Social Sciences
Practical and Applied Sciences
- !exercise-and sports-science@mander.xyz
- !gardening@mander.xyz
- !self sufficiency@mander.xyz
- !soilscience@slrpnk.net
- !terrariums@mander.xyz
- !timelapse@mander.xyz
Memes
Miscellaneous
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Limits still are not intuitive to me. Whats the distinction here?
Different slopes.
On top you kill one person per whole number increment. 0 -> 1 kills one person
On bottom you kill infinity people per whole number increment. 0 -> 1 kills infinity people
You can basically think of it like the entirety of the top rail happens for each step of the bottom rail.
If people on the top rail are equally spaced at a distance d from each other, then you'd need to go a distance nd to kill the nth person. For any number n, nd is just a number, so it'll never be infinity. Meanwhile the number of real numbers between 0 and 1 is infinite (for example you have 0.1, 0.01, 0.001, etc), so running a distance d will kill an infinite number of people. Think of it like this: The people on the top are blocks, so walking a finite distance you only step on a finite number of blocks. Meanwhile the people on the bottom are infinitely thin sheets. To even have a thickness you need an infinite number of them.
There are an infinite amount of real numbers between 0 and 1. On the top track, when you reach 1, you would only kill 1 person. But on the bottom track you would’ve already killed infinite people by the time you reached 1. And you would continue to kill infinite people every time you reached a new whole number.
On the top track. You would tend towards infinity, meaning the train would never actually kill infinite people; There would always be more people to kill, and the train would always be moving forwards. Those two constants are what make it tend towards infinity, but the train can never actually reach infinity as there is no end to the tracks.
But on the bottom track. The train can reach infinity multiple times, and will do so every time it reaches a whole number. Basically, by the time you’ve reached 1, the bottom track has already killed more people than the top track ever will.
Great explanation, I'd just like to add to this bit because I think it's fun and important
Or any new number at all. Between 0 and 0.0...01 there are already infinite people. And between 0.001 and 0.002.
What I still don't understand is where time comes into play. Is it defined somewhere? Wouldn’t everything still happen instantly even if there are infinite steps inbetween?
I guess it could be implied by it being a trolley on a track, but then the whole mixing of reality and infinity would also kind of fall apart.
Is every person tied to the track by default? If so, wouldn't it be more humane to just kill them?
Worse. It will kill an infinity every time it will move any distance no matter how small.
For every integer, there are an infinite number of real numbers until the next integer. So you can't make a 1:1 correspondence. They're both infinite, but this shows that the reals are more infinite. (and yeah, as other people mentioned, it's the 1:1 correspondence, countability, that matters more than the infinite quantity of the Real numbers)
There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn't hold.
The only simple intuition for the uncountability of the reals I know of is Cantor's diagonal argument.
You can assign each rational number a single unique integer though if you use a simple algorithm. So the 1:1 correspondence holds up (though both are still infinite)
There are also an infinite number of rationale between two integers, but the rationals are still countable and therefore have the same cardinality as the naturals and integers.
Makes sense, thanks!