Limits still are not intuitive to me. Whats the distinction here?
Comment on IT'S A TRAP
mumblerfish@lemmy.world 3 weeks ago
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.
buffing_lecturer@leminal.space 3 weeks ago
NoneOfUrBusiness@fedia.io 3 weeks ago
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.
mrmacduggan@lemmy.ml 3 weeks ago
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.
anton@lemmy.blahaj.zone 3 weeks ago
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.
carmo55@lemmy.zip 3 weeks ago
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.
mrmacduggan@lemmy.ml 3 weeks ago
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)
buffing_lecturer@leminal.space 3 weeks ago
Makes sense, thanks!
turdcollector69@lemmy.world 3 weeks ago
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.
PM_Your_Nudes_Please@lemmy.world 3 weeks ago
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.
schema@lemmy.world 3 weeks ago
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?
porous_grey_matter@lemmy.ml 3 weeks ago
Great explanation, I’d just like to add to this bit because I think it’s fun and important
And you would continue to kill infinite people every time you reached a new whole number.
Or any new number at all. Between 0 and 0.0…01 there are already infinite people. And between 0.001 and 0.002.
bampop@lemmy.world 3 weeks ago
That’s still not doing it justice. If there were one person for every rational number there would be infinitely many in any finite interval (but still actually no more than the top track, go figure) but the real numbers are a whole other kind of infinite!
Klear@quokk.au 3 weeks ago
and will do so every time it reaches a whole number
It will kill an infinity every time it will move any distance no matter how small.
HeyThisIsntTheYMCA@lemmy.world 3 weeks ago
eleijeep@piefed.social 3 weeks ago
The bottom one will kill an infinite amount of people in finite time.
instantaneously FTFY
ivanafterall@lemmy.world 3 weeks ago
I’m going bottom.
NOT LIKE THAT. Not like sexually. I just mean I want to kill all the people on the bottom with my train.
ConstantPain@lemmy.world 3 weeks ago
Too late! Now bend…
a_person@piefed.social 3 weeks ago
So still sexually