'>>16141942
As a corollary, the implication of Gabriel's horn is that there exist geometric objects with no defined centroid lmao.';

'>>16141942
>Clear violations of Stokes theorem
how? I see no mention of a curl or or the integral of any field';

'>>16141951
I'll curl one out on you. There. There's a mention of a curl. fagite.';

'>>16141952
the finitist, everyone';

'>>16141951
Stokes theorem is more general than that calc 3 garbage.';

'>the unit pseudoscalar i with i^2 = -1 is a number
>Riemann surfaces and "complex line bundles" are 1-dimensional
>doing geometry over the "complex numbers" isn't a fraudulent waste of time';

'>>16141962
Doesnt matter because theres still no mention of curl or fields or of anything. The example being given (gabriels horn) is in 3D. Theres no contradiction of anything';

'>>16142013
>Gabriel's horn doesn't mention Stokes theorem in its construction
>Ergo there's no way it can contradict Stokes theorem
Are you brain damaged?';

'>>16142017
>Ergo there's no way it can contradict Stokes theorem
There is no mention of any contradiction of stokes theorem. This doesnt mean some contradiction cant exist, but no one is mentioned. So as far as i can tell theres no contradiction.';

'>>16141942
Who said you can apply the Stokes theorem to any type of surface you retard? Go read the theorem again.';

'>>16141965
>1-dimensional
Mmm, univector.';

'>>16141942
Another deboonker trying to find flaws in what 160+ IQ people created with his 130- IQ kek.';

'An infinite surface doesnt mean that an integral over that surface is also infinite';

'>>16141965
i thank god that you will never amount to nothing within your life, filth';

'>>16142013
how would you know that a theorem is being contradicted when you don't even know the theorem';

'>>16141942
0! is 0 (not one) because the notion of organizing a non-entity is nonsense without premise.';

'>>16141942
Hilbert's infinite hotel paradox is a really really poor analogy. The premise of it being completely full prevents his solution working. If every room is full then no room is empty which means no amont of hand waving or kicking the problem far out to the horizon will let another guest enter and get a room (without evicting someone permanently).';

'>>16142051
If it has infinite surface area then it can fit infinite stuff, as long as one accounts for the infinitesimal. To say otherwise its to fundamental misunderstand something real.';

'>>16142198
He's probably a math minor or taking some junior level math class, and views math as gospel without understanding limitations of theorems kek';

'>>16142198
I never said the theorem cant be contradicted in principle, just that no contradictions are being presented by the OP.
>>16142255
Irrelevant
>>16142250
>If it has infinite surface area then it can fit infinite stuff
So what? You are saying something that is true but it has nothing to do with anything that is being discussed.';

'>>16142250
>t. doesn't know what converging and diverging means';

'>>16141942
>Clear violations of Stokes theorem, not that they give a shit
It's not. You're just stupid';

'>>16142353
>So what? You are saying something that is true but it has nothing to do with anything that is being discussed.
It's relevant to Gabriel's horn?';

'>>16142477
So what?
Here let me write it: Gabriel's horn.
What the fuck does it have to do with anything? KYS retard';

'uh-oh shots fired
https://www.youtube.com/shorts/cYvzZrHvkIM';

'>>16142489
It's mentioned in the OP';

'>>16142246
We define 0!, the product of the first 0 natural numbers, to be 1 because we define all empty products to be 1, because the product of A and B for A and B nonempty is the product of A times the product of B, and the only way to keep that consistent if either A or B is empty is of the empty product is the multiplicative identity, 1.
Strangely you never see people get this caught up on empty sums. People accept that if you're going to say the sum of no numbers is something then that something is 0. I guess they just never think about why.';

'>>16142923
Schizobabble';

'>>16142248
>without evicting someone permanently
Whose getting evicted permanently? If a guy lives in room n, then you can just move him to room n+1, and so on.';

'>>16141942
>i don't understand complicated math and that means it's wrong.

thank fucking god we don't all go to you for marh advice lamo.';

'>>16143023
>>16142248
>>16141942
You know what's interesting? When paradoxes arise in physics or chemistry, there's a RESOLUTION to the paradox by exposing a faulty assumption.

When paradoxes arise in math, mathematicians instead say "oh that's just an unintuitive result" and double down on the assumptions that causes the paradox.

What a pathetic field of study.';

'>>16143033
>When paradoxes arise in math, mathematicians instead say "oh that's just an unintuitive result"
We do though? Zermelo Franklin set theory was developed to resolve Russels paradox. Also, if you don't think physics has unintuitive results I want to know where you've been for the last 100+ years lmao';

'>>16143033
physics is math, you fucking cuck. it's FULL of paradoxes. go suck your own cock elsewhere.';

'>>16143033
i got a horn for you to blow on';

'>>16143033
Kek any post that has the mathfags seething is gold. Good post.';

'>>16142250
>If it has infinite surface area then it can fit infinite stuff
This is obviously not true. To give a lower dimensional example, the area between the line y=(1/2)^x from 0 to infinity and the x axis.

From 0 to 1 it will have a value less than 1. From 1 to 2 it will have a value less than 1/2. From 2 to 3 it will have a value less than 1/4. And so on and so forth. The total area can never be more than 2 (it's literally the most famous convergent series there is), but the length of the line is infinite and the height at each point on the line is never 0.

Infinite line, finite area under it.

And what's this? You can rotate that line around the x axis to get a trumpet which is contained entirely in a series of cylinders whose total volumes also converge!?! What were the odds?!?

1. The odds were 1.';

'>>16143175
>the length of the line is infinite
Proof?';

'>>16143571
it's larger than any natural number';

'>>16141942
Sounds like you got filtered by limits';

'>>16143033
in math can you can create whatever assumptions or axioms you want and paradoxes are hecking valid for those rulesets. math doesn't tie itself down to the real world thats its advantage, there are no faulty assumptions, just different rule sets, but yes these paradoxes don't work in the real world and that's interesting because it exposes how different the real world is to the most intuitive assumptions and axioms. It's the real world that is unintuitive and bizzare not the constructed math worlds.';

'>>16143596
Proof?';

'>>16143618
>Internal inconsistencies via paradoxes is an advantage because it doesn't describe reality; ergo reality is the bizarro world not my heckin valid math
Jesus fucking Christ.';

'>>16141942
>"infinity + 1" isn't greater than infinity!
>also, some infinities are bigger than others
gaslit
>you can't divide by zero, idiot!
>also, actually, you actually can divide by zero, idiot!
manipulation tactic to control you';

'>>16143625
Jesus Christ is my Lord and Savior. God raised Him from the dead!';

'>>16142923
>because the product of A and B for A and B nonempty is the product of A times the product of B, and the only way to keep that consistent if either A or B is empty is of the empty product is the multiplicative identity, 1.
I'm going to be honest, I don't understand what you just said and it seems fishy. I've yet to make up my mind about the matter because not understanding something and rejecting it out of hand is stupid. But I do suspect that what you said doesn't actually add up.

>>16143023
N+1 is full. The entire premise of the paradox, the very nascency of the thought experiment (or whatever you'd call it) is that there are infinite guests in infinite rooms. All rooms are in state 'full'. No rooms are in state 'empty'.

>>16143033
That's basically my stand as well. So far in my search for resolutions to some things that don't add up in math it seems to boil down to "Because I said so" (or some other arbitrary personal attribution) or "It has to or the models wouldn't work".';

'>>16143175
not a good example though since the area of a line is 0 even if it's infinitely long
and rotating the line around the x-axis creates an narrowing cylindar where the surface gets smaller and smaller just like the area under .5n gets smaller and sums to a finite amout. the area under the 1dimensional curve is 2dimensianal, yet finite. the surface area of the cylinder is also 2dimensional. how is it not finite?';

'>>16143632

>Picrel

>Use the language of the Judeo-Semites who killed Jesus to convey a love for Christ.

And I will promote my love for humanitarianism with human blood.';

'>>16143785
Hebrew was invented by Jesus.';

'>>16143646
>N+1 is full
It is? I thought the resident of N+1 moved to N+2, leaving N+1 empty';

'>>16143977
I feel like this is a skill/rationality filter.
If N+1 moved to N+2 then what of N+2's occupant?

Do you not see how evicting people is evicting people no matter if you stop at 3 evicted people or pushing the matter far, far out? Literally someone is always going to be standing in the hallway to accommodate this new person. The fact that its very very far away is morally moot.';

'>>16144046
>what of N+2's occupant?
They also get moved to (N+2)+1=N+3
>evicting people is evicting people
I guess we just have different understandings of eviction then. Nobody's permanently getting kicked out, they just change rooms
>Literally someone is always going to be standing in the hallway to accommodate this new person
Who? If this person exists he must have a number. Even if he's in room 100! there's a room 100!+1';

'>>16144053
>They also get moved to (N+2)+1=N+3
That's just sweeping the problem under the rug (or in this case, kicking the problem down the road while you hope to remain farther and farther from it). I don't have any way to convince you of this by means of communicating. It's a self-evident truth.
>Nobody's permanently getting kicked out, they just change rooms
Max capacity + 1 means that someone is roomless. If the hotel is completely full then someone will be without a room. How do you not understand that?
>>16144053
>Who? If this person exists he must have a number. Even if he's in room 100! there's a room 100!+1
Holy shit';

'>>16144277
Mathematicians don't care about reality. It's somewhat sad. I think this anon hit the nail on the fucking head.
>>16143033';

'>>16144277
>Max capacity + 1
Are you saying that there's a biggest number? Look up the definition of "infinity" and stop wasting people's time lol';

'>>16144353
>Look up the definition of "infinity" and stop wasting people's time lol
>Infinite hotel is infinitely full, completely booked up
>But there's is an empty room you just can't number it
Is it insanity? Is the problem that you are literally insane?';

'>>16144431
I don't really know how to explain this. It always seemed straightforward to me

Let f be the sequence of occupied rooms
f = 1, 2, 3, 4, ...
If you shift every occupied room up by 1 you get
f+1= 2, 3, 4, 5, ...
There is now an unoccupied room, room 1 to be specific.
>>But there's is an empty room you just can't number it
Yes you can, it's room 1
>Is it insanity?
Ig every mathematician's at least a little crazy, but you still need them anyway for the modern world to work';

'>>16144448
>Ig every mathematician's at least a little crazy, but you still need them anyway for the modern world to work
I don't think you do. If all the mathematicians dropped dead, what exactly would change? Applied mathematicians often have phds in physics or engineering, not math. My best math professors all had phds in physics.';

'>>16144466
We wouldn't get stuff like an O(nlogn) FFT or the simplex algorithm or search engines or whatever. Cryptography would gradually become obsolete and there'd be nobody around to improve it. It wouldn't be catastrophic but the rate of innovation would slow down greatly';

'>>16143571
>Proof?
It's constructed to go to infinity? I don't know what you want from me. It's definitionally infinite. The x axis doesn't end, so it doesn't.

>>16143660
>not a good example though since the area of a line is 0
And the volume of a surface is 0. What the fuck are you even arguing? I said it was a lower dimensional example.';

'>>16144448
There is now an unoccupied room, room 1 to be specific.
At the expense of SOMEONE SOMEWHERE.
You cannot say that's not the case without admitting the the hotel wasn't actually full of people / empty of unoccupied rooms. I've decided that it actually is insanity that is your problem. I'll still talk to you though since I'm real patient and also maybe someone who isn't insane will see both sides of this conversation and realize who is right and who is wrong.

If there is an unoccupied room, then the hotel was never full. If the hotel is full, then the beginning of the thought experiment there wasn't a free room, the isn't a free room, and there will not be a free room without (try to keep up because this is the important part): the creation of a brand new room that didn't exist at the time of the start of the thought experiment, the eviction/erasure of an occupant, or the invalidation of the premise.

It's literally not rocket science and, since the thought experiment is in words, one need not even be a mathematician to interface with it authoritatively. Full means empty of emptiness. Empty means empty of fullness. It's either full or it's not full. Make up your mind and act like someone with integrity.';

'>>16144506
>It's definitionally infinite. The x axis doesn't end, so it doesn't
Then so is the area bounded since the x axis goes forever.';

'>>16144507
>the eviction/erasure of an occupant
And that's exactly what happens. The person in room 1 gets moved to room 2, and so on for infinity. We're going in circles now, but I challenge you to find a single person who got evicted from the infinite hotel entirely. And yet, there is a new room
Infinity+1 = infinity, and if you can build a mathematical system where that isn't the case, you will likely be the greatest mathematician to have ever lived';

'>>16144548
He's saying the hotel is either full or not full. It's mutually exclusive. Your take implies it's simultaneously full and not full, where it's by definition full but can permit more tenants. It's ludicrous on its face to anyone who isn't a schizophrenic mathematician';

'>>16143629
>"infinity + 1" isn't greater than infinity!
infinity + 1 is just 1 - infinity';

'>>16144554
>every room is full in an infinite hotel
>shift everyone to the room to the right
>room one is now empty
I genuinely don't see the point of confusion here lmao.';

'>>16144554
Thank you, anon. There's something fundamentally wrong with the way these people think (or don'think). They literally just talk in circles. This is why, I imagine, a lot of autistic people say non-autistics are the problem when it comes to communicating.';

'>>16144579
Would also explain why math attracts turbo autists. I'm talking the socially inept tards.';

'>>16144431
*sigh*, what is greater, the set of natural numbers or the set of rational numbers?, the answer to this question will reveal a lot about you';

'>>16144466
do you really think that applied mathematicians aren't a subset of all mathematicians and as such would be impervious to your hypothetical "all the mathematicians dropped dead" scenario?';

'>>16144507
>At the expense of SOMEONE SOMEWHERE.
boy it does feel like infinity ain't for some people, but eh, oh, as an aside, how would you have felt if you hadn't had breakfast this morning?';

'>>16144507
ever heard of a bijection?
>>16144561
in the real projective line inf is still absorptive';

'>>16144683
>boy it does feel like infinity
People who use it as a cope and refuge from rational application of mind';

'>>16144691
finitism isn't rational, that is a certainty, for it is anti-human';

'>>16144687
is this "absorptive property" in the room with you right now?';

'>>16144727
n*0=0, zero is multiplicatively absorptive, infinity is additively absorptive as well on top of that, you baboon';

'>>16145162
Infinity isn't a number. At least that's what the mathematicians claim when it's convenient. Then they claim you can add numbers to non numbers. Therefore pizza + 1 = pizza.';

'>>16145164
True, this also applies to the sum of natural numbers being -1/12.
Algebra on infinite makes no sense even in currently accepted fundamental axioms of fürs and second order logic as well as other set theoretic axioms';

'>>16145164
>Infinity isn't a number.
it is, they just say it isn't because retards cant even cope with literal multiplication, let alone infinities
>>16145184
re-educate yourself
https://www.youtube.com/watch?v=beakj767uG4';

'>>16145630
>it is, they just say it isn't
Thank you for admitting mathematicians are liars';

'>>16145184
I'm becoming increasingly convinced that infinity is a pathology of math. In physics it may seem like we take infinity but we don't. In actuality we normalize everything then if x << 1 we neglect it. Physically it amounts to something like d << D. Perhaps the mathematicians have something to learn from the physicists.';

'>>16146614
watch the video and stop being stupid >>16145630';

'>>16147921
Stop feeding the trolls and bumping this retarded thread';

'>>16147921
I watched the video. It was a mathematician who published a paper taking a lesson from physicists. Funny how you call me stupid while providing evidence that what I said is right.';

'>>16141942
Infinite surface is a lie when the minimum planck length exists. You can only make structures with features so small.';

'>>16148959
>He believes in a minimum length
>He can't conceive of the infinitesimal
>He arbitrarily BELIEVES what he has heard';

'>>16148959
Thread is about math, nigger. It's nice that you know what a Planck length is though. Good job.';

'>>16141942
wait until you hear about fractals, finite area and infinite circumference!';

'>>16145162
>zero is multiplicatively absorptive
and how do you justify this claim?';

'>>16150397
>infinite circumference!';

'>>16141942';

'>>16150920
simple, the leg with the imaginary length is imaginary, therefore there is no actual triangle so the hypotenuse doesn't exist either and has length 0.';

'>>16148978
>>16149042
>Autists can't recognize where pure math doesn't reflect reality
You're like a baby using Newtonian physics at the subatomic or galactic level. It doesn't apply.

Gabriel's horn doesn't work because it gets so narrow that it no longer acts as a volume.

I understand the infinitesimal, and I know that the infinite horn will not blow.';

'>>16151506
>>16151506
>Gabriel's horn doesn't work because it gets so narrow that it no longer acts as a volume.
actual schizophrenia. so you're saying there is no volume bounded by gabriel's horn? that's equivalent to saying it has infinite volume, which is what op says.';

'>>16150920
>Make X,Y,Z compound triangle
>Abstract X and Z into imaginary complex number Y = a+b*i
Congratulations you rotated a path into three dimensions. It is very clever, but don't pretend it is something more than clever.';

'>>16151509
Gabriel's horn is the integral from 0 to infinity where the area under the curve is a finite and calculable number. You then rotate the curve to make a horn or "curved conical-ish" shape that is infinitely long and pi*r^2 section of volume to convert that surface area into a finite volume. The math is very simple.

However excluding any difficulty of considering the infinite length of such a volume (with or without a physical enclosure to the volume) the diameter of the long tail will become so small it will not be usable for any purpose, to include the passage of a single photon or other particle or wave.

If you considered the appropriate theoretical physical limit, Gabriel's horn is truncated to a specific length and a different volume which is also affected by the nature of the volume and enclosure, if any.';

'>>16151520
>math is very simple
Well if it's simple, it must be accurate and true!
The earth is flat. Why? It looks flat. Shrimple as that.';

'>>16151527
What's fun is that mathfags go on about infinite lengths on a Cartesian plane when astronomy finds that space is warped and not straight at all. (Although current theory on observations is an overall Cartesian curl vs hyperbolic or closed).

Brainlets who mistake model math with reality are most of academia.';

'>>16151506
>Gabriel's horn doesn't work because it gets so narrow that it no longer acts as a volume.
That's a viewpoint that I think you can't substantiate. I think you only hold it because you actually cannot conceive of "that which is infinitesimal" or "that which is very small yet not zero" in a way that is in line with reality. That's a limitation that you should overcome because if you do you'll be able to conceive of and seek things that are more excellent than what you currently regard as the natty limit of reality.';