What is the most abstract, difficult to fully see and understand, or counterintuitive mathematical theorem you know?

>He can't even spell his favorite memes right

The correct answer is the countability of computable numbers.

...

The wiki on pigeonhole principle
Says something that is ludicrously false. That at least 2 people in london have the same number of hairs on their heads. What if there were only 10 people in london? The chance of any 2 of the 10 people having the same number of hairs on their head is infinitessimally small. Adding people to london makes it more likely, but it is by no means certain unless youre a faggot

It's a there's no argument to be had. Portals preserve the momentum of whatever goes through it.

If you say that portal a is moving and from that frame the block has momentum then you have to say that portal b is moving just as fast.

If there were 10 people in london it wouldn't work unless nobody had more that 9 hairs. It's almost as if you didn't read the fucking paragraph.

>What if there were only 10 people in london?
there aren't fucking 10 people in london you mong

The answer I came up with is that you're ending up with one part of the cube holding forward momentum, and one part of the cube with none. As the cube continues to pass through, the momentum to no momentum ratio increases until it is wholly affected by the momentum. B is the answer

Nothing about the pigeon paradox seems false. I'm not even memeing when I say I came up with it in my head in like 4th grade

*pigeonhole principle
whoops

No, that's wrong and doesn't make sense from a physics perspective. There is no momentum in the block unless you lock at it from the frame of the orange portal, and if that's the frame you're looking at it from then necessarily the blue portal has the same velocity, when the block pops out of the blue portal it comes out going velocity a when the portal is going -a, and therefore the block isn't moving at the end of the scenario.

The cube doesn't "gain" momentum through nothing happening.

you're retarded

In my experience a lot of people come up with it by themselves. I've done a lot of stuff with contest programs and a fairly large percentage of people who've never seen the pigeonhole principle before will use it almost unconsciously if you give them a simple problem about it.

You, you are wrong. There is no force acting on the box UNTIL the portal begins to pass over it. On the other side, at the blue portal, the cube is coming out and it is moving. It has momentum, but due to the paradoxical nature of portals it also has a part with no momentum. Eventually the entire cube is moving because no part of it is still static

Does that make sense?

Yeah I'm not claiming I'm a genius or anything (i'm not even STEM heh) but it's really intuitive.

No, lol it doesn't because that's wrong entirely.

There's no force at all acting on it, a portal doesn't do anything to an object, imagine that it's a hula hoop (because that's what it is).

Momentum is preserved, you aren't adding momentum to an object when you pass it through a portal. You're acting like the act of passing through a portal for some reason makes something move. If you jump through a portal it's as though you're appearing at the spot of the second portal with the same conditions as how you entered the previous portal.

There is a concept you aren't grasping here. It is different than just slamming a hula hoop around the cube. Look at the cube from the perspective of the blue portal. It is MOVING. It has mass, and it is moving, so what does that leave us with? Inertia.

You can't think about this in terms of traditional physics because the concept of portals breaks physics. We are dealing with an object that is not moving, then slowly bit by bit enters the state of moving. It will have the same speed at the speed of the orange portal coming down

No, no it won't. There's no point in talking about this if you just go "well physics doesn't work so this which doesn't make sense makes sense"

If you pick your frame of reference as the blue portal, then the block is not moving. Why would it be? The orange portal is the thing that's moving.

It is not different for the reasons I outlined before, momentum of the object is conserved, which means that velocity in = velocity out, and from any inertial reference frame it's the same thing. If you take the frame as the block is not moving, then it's not moving when it gets out of the portal.

If it is moving (in your frame because you take the orange portal as the origin) then the blue portal is moving by the same argument.

What's the speed of the blue portal? Same as the block, in the opposite direction.

It doesn't "bit by bit" enter the state of moving, you're changing the frame without changing how you look at each object.

There's nothing I'm not grasping because there's nothing to grasp.

I feel like I'm getting baited.

I'm not baiting you. The portal isn't just being viewed from two different perspectives, it's actually moving from one to the other. From the blue portal you see the cube emerge at a very fast speed. What force acts on it to stop it from continuing?

Because what you're seeing isn't the cube moving quickly, you're seeing the orange portal moving quickly.

You don't see it emerge at a fast speed, all you see is the hula hoop going down fast. The reason it looks like its coming at you quickly is the same as why it would look like it's coming at you quickly if you were on the underside of the piece that's coming down.

Portal is just a connection between two points in space, that's it.

You aren't listening to me when I say "from the perspective of the blue portal"

Because what you're seeing isn't the cube moving quickly, you're seeing the orange portal moving quickly.

That is from the perspective of the blue portal. I literally only addressed that the entire time in my last post.

WHAT THE FUCK DO YOU MEAN

You can't see the orange portal from the perspective of the blue portal, you see the cube and the stand and the ground below it rushing towards you!

from the prespective of the blue portal the orange one is stationary

Yes that's what it looks like, but what I mean by you're seeing the orange portal, I mean that the motion your eyes are calling the motion of the block is the motion of the portal. You're not seeing it rush toward you, you're what the orange portal sees, which is itself rushing towards the block.

It's literally the same as a hula hoop/open window/whatever metaphor you want to use.

The portals aren't two different entities, space immediately after and immediately before are different, but the portal itself is just a hole in space.

A really simple way to think about the problem is that it's a hula hoop, and it's accurate based on all the available evidence in the game. There's no reason for the object to come out at any speed, including A really. The object would be totally stationary, just on an incline now.

obviously [math]e^{i\pi}=-1[/math]

inb4 newfaggot

but from both the orange and blue portals perspectives, the cube is moving. Only from the cube's perspective is the cube not moving.

yer a brainlet harry

Again, think of it like a hula hoop. Yes from the hoops perspective the block is moving, but only from that perspective is it moving, once the orange portal stops moving, so does the block.

Let's say that the block is on a thin pole rather than a flat surface which stops the top portal, then the block would be moving out of the blue portal at the same speed the orange was moving down, but everything is, not just the block but the pole too, and when the portal accelerates to a stop, then so does the block+pole combo at exactly the same rate.

Based on this same line of reasoning, the pole is the surface, and the acceleration happens right when the two surfaces meet.

It's like in space, if you're drifting towards a ball or the ball is drifting towards you is literally meaningless, there's no difference between the two. Everything depends on the frame of reference.

Are you saying the velocity of the portal relative to the box doesn't matter at all?

how come the box doesn't come flying out at the speed of the earth's movement in space?

>it's another "argue about how portals work" episode

>comparing rocks eroding to genetic mutation and natural selection

Because the portal is too, or rather the point in space that constitutes where the portal is is always moving at that speed. Points A and B are not different points, they are the same spatial point, I mean it's a planar surface not a point, but same idea it's a 2D shape within the 3D world that connects two locations in 3D space.

The portal is not a thing (meaning has mass), the locations where the portals are attached to the earth are things.

Alternatively, it's because portals don't work the way physics says they should. Even if they were two stationary points, meaning wall A and B were where the portal was attached, if the walls are perpendicular then there's no reason (i can come up with) why the block doesn't fly out at the earth's speed.

This is where I think portals violate reality.

If you take us to be a 3D reality moving through 4D space, and a portal to be essentially a doorway into 4D space that can only spit us back into a 3D space (think how a no depth circle does this in a 2D to 3D analog.) Then a lot of the problems with regards to conservation of momentum/energy and portals goes away. That's why the momentum arrows point in different directions with no acceleration happening, because they've changed the 3D space orientation due to it having left 3D space (and immediately reentered).

I didn't even know this had a name for it, I thought it was common sense.

Counterintuitive results in decreasing order of counterintuitiveness:

Zeta function universality
Riemann Rearrangement theorem
Banach-Tarski
connected doesn't imply path-connected
the existence of the sporadic groups (the Monster, etc.)
there is a function discontinuous everywhere that satisfies the IVT (Conway's 19 function)
Kuratowski's closure-complement problem
Brouwer fixpoint theorem
Hairy ball theorem

>i came up with it in 4th grade therefore it's real
found the asperger brainlet

Banach-Tarski is pretty trivial if you understand how it works.

That really isn't counterintuitive though

You just added imaginary friend to the equation. It really changes nothing, only pushes everything 1 step away. At least we have some profs of evolution and fossils of animals. Do you have and fossil of good, anything besides those fairy tales called bible that have less logic in that starwars saga.

-1/12

e^πi=0

Maybe hard to prove for an undergraduate. But counter-intuitive?

>x is trivial if you understand how it works
literally everything

kek, this

Thirding. Honestly can't understand how anyone could think any differently.
What's the alternative? You have more objects than containers, so you pretend the objects don't exist?

No, I'm convinced that not intuitively understanding it is either a troll or I'm such a massive brainlet I'm missing something because I literally can't think of how someone would arrive at a different conclusion.

>connected doesn't imply path-connected
what in the absolute fuck

math.uconn.edu/~kconrad/blurbs/topology/connnotpathconn.pdf
im not really understanding why the "deleted infinite broom" can be considered connected

>found the brainlet

i don't know what you're asking, but the usual example is topologist's sine curve plus a segment

I proved it in calc 2.

it appears on page 5 in the same document actually, where he gives the example of the point (0,0) adjoined to the curve sin(1/x) as connected but not path-connected

......and suddenly, i've got it

It was counterintuitive for, not particularly hard to prove after some looking at it.
It's just one of those theorems that I looked at and thought "Nah that can't be true" and started trying to list counterexamples.

It was also one of my first proofs where I started to understand why mathemagicians like proving proofs.

I'm self-taught btw, not in school.
Most of the other theorems in this thread seem to be why I hate proofs. Shitty definitions -> shitty unintuitive theorems.

The despair code?

did you even read the passage you're referring to?

Not a theorem, but the mathematical concept that always fucks with me is the Axiom of Choice. I'll get caught up at times forgetting to use it or questioning whether it is necessary for proofs. It's another one of these things that seems so obvious it is easy to forget that you have to apply it.

If you're not working in pure set theory, you really don't have to mention using choice in your proofs.

>he doesn't get it

are you fucking retarded? have you ever seen a six-pack with seven beers in it?

Abstract Algebra is hard, but that theorem is easy bro. Wyd?

It kinda depends on how the rules of portals works, honestly. Option A is intuitive to me though.

Bartowski-Krieghoff theorem. I have a few years worked hard to prove it, with no luck.

how do you determine what A and B are if you only know C?

You made up that name.

I guess it wasn't that difficult to fully see after all.

The set of valid values for a and b describes a circle with c as the diameter.

Should be portal B. If its moving normal to the point of intersections in A than it should process a mirror image in B with respect to 180 degrees in the same way optics work

> difficult to fully see and understand
Almost all argumentum reductio ad absurdums are difficult to see and comprehend. It's because they are absurd and don't exist. The more fundamental your geometrical understanding is the more absurd they become. I.27 of Euclid for example doesn't make sense at all, but that's because it isn't supposed to.

Usually when Archimedes makes this argument it's all theoretical and he doesn't illustrate the points, but Archimedes' argumentum ad absurdum literally CENTERS around that proposition in Elements which states that you can theoretically take the remainder or the difference between two numbers and add it onto itself so its less than the former and larger than the latter.

Qualia not in the set of Reals.

Since it was unclear, did the yellow portal stopped half way through the box, I fixed that for ya.

One other thing.

Dude you played "musical chairs"

Autism. Literally.

>its a portal thread
lol Veeky Forums

If the air pressure is equal on both sides, wouldn't it resist the "incoming" air? If we consider air displaced by the slab surrounding the moving portal negligible, does portal motion generate a pressure gradient?

The most complex and irritatingly large equation I've encountered was theoretical physics (specifically the Higgs Boson theory In its early days) now that was a monster of an equation lol there was so much work and not enough brains.

en.wikipedia.org/wiki/Pigeonhole_principle

shit man

u fall for bait like a moth to light

you mean flame right?

10/10

Super easy corollary of Ramsey's theorem.

Yes, it's me, Chris! What's up my dude!