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Why I cannot divide by 0
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kai99 wrote:
but the cake is a lie
I just found to never run out of cakeskai99 wrote:
cake goes to infinityBlitzfrog wrote:
The limit, as the number of people I'm dividing cake for approaches zero, the number of slices approaches...
Wait, wouldn't you eventually end up with a cake that's untouched? Like, at the limit there won't be any people to give the cake to... (I don't think this is a very good analogy for why you can't divide by 0.)
The old fashioned notion of dividing a whole slice for N people is not going to do us good in this, we need to break the problem down to its core. When you are slicing a cake, you are taking and series of angles of a circles in parts and distributing them one by one. The procedure is the following: You take the whole 360 deg angle and divide it by the number of people you want to give it to, then you trace that much from the starting point around it, and give that much you traced to the first person. Then repeat until you got no cake left. So consider this:Blitzfrog wrote:
The limit, as the number of people I'm dividing cake for approaches zero, the number of slices approaches...abraker wrote:
As a workaround, take the limit of the thing you are trying to divide the thing by 0 and divide it by x as x approaches 0
You have 2pi of cake and need to divide it by one person. Ok: (2/pi)/1 = 2/pi, a whole cake. Here you go one person!
What about half a person? (2/pi)/0.5 = 4/pi or 2 wholes. Right? Wrong! You just go around once, and obviously the rest doesn't matter since you traced the whole, but for the sake of math we will trace a full circle again. The whole cake has been traced around anyway and the half person gets the full cake
What about a third of a person? Same you just go around and stop where you went around already, effectively making no difference.
What about Infinity? Same no difference. Whole cake.
Does this work for 2 people, you, a skeptical reader might be now wondering, now concerned about the nonsense I wrote. Well yes, idiot reader, it does work. Here is how: (2/pi)/2 = pi or half of a whole. So you give the traced amount to the first person and continue tracing (2/pi)/2 for the second person. Another half!
And so, quod erat demonstrandum
Edit: What happens if you try dividing by infinity:
my god
why would you have 2pi of a cake tho
why would you have 2pi of a cake tho
Well assuming its a regular cylindrical cake
It should have 2pi*r^2*h of edible volume available.
It should have 2pi*r^2*h of edible volume available.
3D is irrelevant when cutting the cake because of the subsection nature of the cut. If you have a 4D knife and cake on the other hand, then would play a role.Rifdi wrote:
Well assuming its a regular cylindrical cake
It should have 2pi*r^2*h of edible volume available.
Why not?kai99 wrote:
my god
why would you have 2pi of a cake tho
This thread is a fathom away from plunging into the abyss of mathematics, I would like to execute a strategical retreat.
Topic Starter
how did it get this complicated
I thought the answer was () (you divided the 0 in the middle and it splited into () )
I thought the answer was () (you divided the 0 in the middle and it splited into () )
I'm sorry I can't take this anymore, I need to tell you the truth.Rifdi wrote:
Did u just
Wow
Im speechless dad
You, my son, are adopted.
*cries in 1x100*_SkyFall wrote:
I'm sorry I can't take this anymore, I need to tell you the truth.Rifdi wrote:
Did u just
Wow
Im speechless dad
You, my son, are adopted.
ill have one planck length of cake
How so? How would you even know what a 4D shape looks like? Let alone cut it. The motion of cutting implies 3D. How do you cut a 2D cake with a 2D knife without going to the 3rd Dimension?? (Slicing doesn't count)abraker wrote:
3D is irrelevant when cutting the cake because of the subsection nature of the cut. If you have a 4D knife and cake on the other hand, then would play a role.Rifdi wrote:
Well assuming its a regular cylindrical cake
It should have 2pi*r^2*h of edible volume available.
Plus, what does a 4D cake even look like?? A 2D cake is pi*r^2, a 3D cake is pi*r^2*h, but the 2 shapes are different. The equivalent of a circle in 3D is a sphere, not some puny cylinder. Note: we can consider a cylinder as 2-2D objects: circles and a rectangle. So what is the combination for a 4D cake??
Cylinder + rectangular prism??(which is the equivalent of 2*circle*rectangle + rectangle*6 in 2D world). Cylinder + Sphere?
First off, it's 2pi radians of a cake. Things need units depending on what you're measuring. For example, when measuring your dick, you would say x dx long. Now if you don't know what radians are, you obviously haven't played enough MMORPG to know what raids are, which means you should go play more. Now since I'm a nice person, I'll explain what radians are. It's basically a unit that we use to see whether we hit the G spot or notabraker wrote:
Why not?kai99 wrote:
my god
why would you have 2pi of a cake tho
First if you cut a 2D cake with a 2D knife, then your are effectively squashing it and not cutting it, because you know, like you said how would that go to the 3rd Dimension? It would make more sense to cut a 1D cake with a 2D knife. A 4D cake is impossible for a 3D being to comprehend, but it would would be a 4D cylinder. Here is a 4D cylinder being rotated in a crossection of 3D space:Blitzfrog wrote:
How so? How would you even know what a 4D shape looks like? Let alone cut it. The motion of cutting implies 3D. How do you cut a 2D cake with a 2D knife without going to the 3rd Dimension?? (Slicing doesn't count)
Plus, what does a 4D cake even look like?? A 2D cake is pi*r^2, a 3D cake is pi*r^2*h, but the 2 shapes are different. The equivalent of a circle in 3D is a sphere, not some puny cylinder. Note: we can consider a cylinder as 2-2D objects: circles and a rectangle. So what is the combination for a 4D cake??
Cylinder + rectangular prism??(which is the equivalent of 2*circle*rectangle + rectangle*6 in 2D world). Cylinder + Sphere?
Please see this post and consider signing up to OT University's OT unit theory course.Blitzfrog wrote:
First off, it's 2pi radians of a cake. Things need units depending on what you're measuring. For example, when measuring your dick, you would say x dx long. Now if you don't know what radians are, you obviously haven't played enough MMORPG to know what raids are, which means you should go play more. Now since I'm a nice person, I'll explain what radians are. It's basically a unit that we use to see whether we hit the G spot or not
This thread will be locked in 6 posts.
This thread will need to be divided by 0 before that happensColdTooth wrote:
This thread will be locked in 6 posts.
You can't divide by 0 because if you could you would be able to make a lot of contradictions.
Using real life examples is bad because you can do a lot of things in maths that don't work in real life.
Using real life examples is bad because you can do a lot of things in maths that don't work in real life.
That's why you you invent stuff to work with the impossible in real lifesilmarilen wrote:
You can't divide by 0 because if you could you would be able to make a lot of contradictions.
Using real life examples is bad because you can do a lot of things in maths that don't work in real life.
But what can't be done in real life would fall in the category of theories or something that is "mathematically possible". Math is the language of the universe and since the universe is real, I don't see why we can't take examples from the real world. It's much more intuitive that way.silmarilen wrote:
You can't divide by 0 because if you could you would be able to make a lot of contradictions.
Using real life examples is bad because you can do a lot of things in maths that don't work in real life.
BUT, If you were saying that certain things in math should be explained in a mathematical way then I agree with you.
omg it's koren
Calculus uses infinitesimal, which is not realisticRifdi wrote:
But what can't be done in real life would fall in the category of theories or something that is "mathematically possible". Math is the language of the universe and since the universe is real, I don't see why we can't take examples from the real world. It's much more intuitive that way.silmarilen wrote:
You can't divide by 0 because if you could you would be able to make a lot of contradictions.
Using real life examples is bad because you can do a lot of things in maths that don't work in real life.
BUT, If you were saying that certain things in math should be explained in a mathematical way then I agree with you.
It isn't realistic but there are real examples for it, black holes for one. All its mass is packed in a single infinitesimal point. Well at least in terms of size the concept of infinitesimal exists.Blitzfrog wrote:
Calculus uses infinitesimal, which is not realistic
Did you just read an article about blackhole online?Rifdi wrote:
It isn't realistic but there are real examples for it, black holes for one. All its mass is packed in a single infinitesimal point. Well at least in terms of size the concept of infinitesimal exists.Blitzfrog wrote:
Calculus uses infinitesimal, which is not realistic
First off, Blackholes don't have mass. Not directly. They're not anything, how can they have mass? Black holes are not objects, they're what happens when you delete a region from the fabric of spacetime. We just talk about them like mass because they, similar to a massive object, exert gravitatational properties to other objects. For example, replace the sun with a black hole the size of the schwartzchild radius of the sun, and nothing about the gravitational effects of nearby objects are effected. Earth will still orbit fine, so will Venus and any other planet in the solar system.
Now you might say "But where does all the mass of the original star go?", well first off, this question was what made Stephen Hawking famous. It was originally thought that the materials of the star are just gone, deleted. But if you do some quantum physics you will know that information cannot be destroyed, and therefore mass cannot just be deleted. What got Stephen Hawking famous was his Hawking radiation, which is literally Black Holes "radiating mass out of itself".
About the singularity, which is what the media says is "Mass squashed to an infinitesimal point". I think what you may be thinking is that black holes are massive objects, collapsed into an infinitesimal point called the singularity, therefore have infinite density.
We, again, have to be careful. The singularity isn't anything. It is not an object, not an event nor a location in spacetime. If you look at the diagrams you find on the internet, it might show the singularity as a point stretching the fabric of spacetime really far down, but that isn't it. Singularities are a hole in spacetime, and this hole makes the geodesics(you can think of geodesics like the "straight lines" of a curved geometry, basically the path an object would follow given by Newton's first law of motion in a curved space) so distorted that it is basically undefined.
Black holes are formed when a sufficiently massive object is collapsed into a volume smaller than the original object's Schwartzchild radius.(I realised this is rather jargon so you can search up about it) This usually means the "mass" of the black hole is equal to the original star that collapsed in the first place. However the horizon of the black hole first forms inside the star, and then expands. This means to external observers, the mass of the object never crosses the horizon. (Nothing ever crosses a black hole to an external observer as light never allows external oberservers to "see" and object crossing). So in this scenario, the mass of the black hole is redundant.
Another problem here is that the equation used to calculate a black hole (Einstein's Field Equations), also allows an empty universe with an eternal blackhole. If you're gonna talk about blackholes, you must include all of them, including this one. But in this case, what are you suppose to say about the mass of the black hole??? There is no mass, as defined by the equation, anywhere.
Glad to see my school works helping, at least in some way. But god dammit, I got carried away...
Me and my big mouth
EDIT: But then again it proves my point that something infinitesimal exists out there.
EDIT: But then again it proves my point that something infinitesimal exists out there.
frog and his chin
That is naive thinking. Alright, yes space is bent infinitely in, but that doesn't mean there is a whole of nothingness there.Blitzfrog wrote:
First off, Blackholes don't have mass. Not directly. They're not anything, how can they have mass? Black holes are not objects, they're what happens when you delete a region from the fabric of spacetime. We just talk about them like mass because they, similar to a massive object, exert gravitatational properties to other objects. For example, replace the sun with a black hole the size of the schwartzchild radius of the sun, and nothing about the gravitational effects of nearby objects are effected. Earth will still orbit fine, so will Venus and any other planet in the solar system.
Let's examine what happens when a photon gets captured be a blackhole. As it passes the event horizon, time no longer ticks, right? Yea. So there are no dynamics going on, right? No. If you see the PBS Spacetime episode on how spacetime behaves inside a blackhole, you would know space starts acting like time and time starts acting like space. Instead of oscillations per second, you need to measure it in oscillation per meter. Let's demonstrate this using an intuitive example, a wave falling towards the singularity. That wave gets pulled toward the singularity, stretching it indefinitely, however it never quite reaches there. It just keep on going there, forever due to the infinite curvature. It is not stretched indefinitely all at once either. You see, if you take a point inside a blackhole intersect by a wave falling in, that point will experience those waves oscillations. However, those oscillations will pass slower and slower as the wave gets stretched more and more. At that point you would get maybe 10 oscillations per meter, then 7, 3, 1, 0.5, etc, approaching to 0 but never quite getting there. You actually need to stay still or move away from the singularity through the space inside a blackhole to have any resemblance of time. This is what it means to have time and space reversed. And as you can see, there is still much happening in there.
Yes, mass isn't deleted because the matter is still there, albeit disintegrated into its component field, may it be the electric field, magnetic field, strong force field, etc and is stretching indefinitely toward the singularity. When the mass radiates out, it's not what inside gets radiated out, but rather due to effects of the strong gravitation field ripping apart virtual particles near the event horizon into matter and antimatter. One matter/antimatter into blackhole, the other half out.Blitzfrog wrote:
Now you might say "But where does all the mass of the original star go?", well first off, this question was what made Stephen Hawking famous. It was originally thought that the materials of the star are just gone, deleted. But if you do some quantum physics you will know that information cannot be destroyed, and therefore mass cannot just be deleted. What got Stephen Hawking famous was his Hawking radiation, which is literally Black Holes "radiating mass out of itself".
Something to clear up. All the energy is being attracted to other energy inside the blackhole, which leads it all towards one point. However, since the energies are concentrated so much, they bend spacetime so much so that the energy as waves have to travel toward the one point indefinitely. Hence the singularity. Another thing, I would say that it's infinite density only relative to an observer outside the event horizon. Relative to an observer inside the event horizon, there is no such point. It's an infinite journey to the center, much like an infinite journey towards the edge of the universe.Blitzfrog wrote:
About the singularity, which is what the media says is "Mass squashed to an infinitesimal point". I think what you may be thinking is that black holes are massive objects, collapsed into an infinitesimal point called the singularity, therefore have infinite density.
We, again, have to be careful. The singularity isn't anything. It is not an object, not an event nor a location in spacetime. If you look at the diagrams you find on the internet, it might show the singularity as a point stretching the fabric of spacetime really far down, but that isn't it. Singularities are a hole in spacetime, and this hole makes the geodesics(you can think of geodesics like the "straight lines" of a curved geometry, basically the path an object would follow given by Newton's first law of motion in a curved space) so distorted that it is basically undefined.
You see it redshifted as it is sucked in. It effectively crosses the event horizon. Though, the actual wave is being stretched from the event horizon to toward the singularity, so some part of the wave is indeed stuck on the event horizon. Time slows down indefinitely there, so the wave becomes highest freq gamma on the event horizon relative to an observer outside the event horizon, though you will never observer that. Relative to an observer inside the event horizon, the wave gets stretched indefinitely toward the "singularity" (which doesn't exist relative to there, just a direction) from an unreachable, external, source.Blitzfrog wrote:
Black holes are formed when a sufficiently massive object is collapsed into a volume smaller than the original object's Schwartzchild radius.(I realised this is rather jargon so you can search up about it) This usually means the "mass" of the black hole is equal to the original star that collapsed in the first place. However the horizon of the black hole first forms inside the star, and then expands. This means to external observers, the mass of the object never crosses the horizon. (Nothing ever crosses a black hole to an external observer as light never allows external oberservers to "see" and object crossing). So in this scenario, the mass of the black hole is redundant.
This would be true if dark energy expands spacetime such that the cosmic microwave background gets redshifted slower than the massive blackhole's Hawking Radiation vaporizes it, allowing the blackhole to get larger as time goes on. Since dark energy seems to be accelerating the universe's expansion, I don't think this will be the case unless universal expansion decides to take another, slower, curve in the next trillion years or so.Blitzfrog wrote:
Another problem here is that the equation used to calculate a black hole (Einstein's Field Equations), also allows an empty universe with an eternal blackhole. If you're gonna talk about blackholes, you must include all of them, including this one. But in this case, what are you suppose to say about the mass of the black hole??? There is no mass, as defined by the equation, anywhere.
At this point I don't know who to trust.
I'll be back after a research.
I'll be back after a research.
First off, this is not what happens inside the blackhole, this is a description of the mathematics inside the blackhole. The infinite curvature of a blackhole just means the geodesics surrounding the blackhole all points inward, so by newton's first law, any object will "remain in the blackhole". The photons that "fall into" a blackhole doesn't get "stretched" by a blackhole. Blackhole isn't you, it doesn't stretch anything, the reason photons "stretch" is because the geodesics are distorted, therefore it takes longer for light to get to you. Similarly, if you travel away from a photon coming towards you, it gets red-shiftedm and clearly you're not "stretching" a photon by moving away from it.abraker wrote:
That is naive thinking. Alright, yes space is bent infinitely in, but that doesn't mean there is a whole of nothingness there.
Let's examine what happens when a photon gets captured be a blackhole. As it passes the event horizon, time no longer ticks, right? Yea. So there are no dynamics going on, right? No. If you see the PBS Spacetime episode on how spacetime behaves inside a blackhole, you would know space starts acting like time and time starts acting like space. Instead of oscillations per second, you need to measure it in oscillation per meter. Let's demonstrate this using an intuitive example, a wave falling towards the singularity. That wave gets pulled toward the singularity, stretching it indefinitely, however it never quite reaches there. It just keep on going there, forever due to the infinite curvature. It is not stretched indefinitely all at once either. You see, if you take a point inside a blackhole intersect by a wave falling in, that point will experience those waves oscillations. However, those oscillations will pass slower and slower as the wave gets stretched more and more. At that point you would get maybe 10 oscillations per meter, then 7, 3, 1, 0.5, etc, approaching to 0 but never quite getting there. You actually need to stay still or move away from the singularity through the space inside a blackhole to have any resemblance of time. This is what it means to have time and space reversed. And as you can see, there is still much happening in there.
First off, what you need to search up is Unitarity. Apparently your main source of information is PBS Spacetime and I'm not sure if they cover it on there, but wikipedia probably does. (It's a good read) Basically it is quantum mechanic's version of conservation law. It is the conservation of information, and an unbreakable law like the conservation of energy. Unitarity is basically what holds the universe together, so it is close to impossible to find a theory that can disprove it. In fact, all theories need to adapt to it because it is so unbreakable. In physics we call these the "minus-1" laws, because it comes before anything else. If we were to violate that, physics would go back to square 1.abraker wrote:
Yes, mass isn't deleted because the matter is still there, albeit disintegrated into its component field, may it be the electric field, magnetic field, strong force field, etc and is stretching indefinitely toward the singularity. When the mass radiates out, it's not what inside gets radiated out, but rather due to effects of the strong gravitation field ripping apart virtual particles near the event horizon into matter and antimatter. One matter/antimatter into blackhole, the other half out.
Now, the mass of the black hole is indeed "in there", but it's not disintegrated into component fields. I have no idea where you got this conclusion from, but no. The idea that information is locked up and inaccessible in a black hole, like a hidden chamber with gold inside, was a view adopted by physicists before Stephen Hawking's ground breaking discovery of Hawking Radiation. (Now for those of you who don't take physics, information doesn't only refer to the matters and energies and what not, but also the properties of them. So for example, an electron has spin, that as a whole is what we mean by information, and all of these information must be conserved.) in 1975, (I believe, don't quote me on that) Stephen Hawking discovered that black holes emit energy, and this emission is now known as Hawking's Radiation. These energy that it emits is the energies contained in the black hole, therefore the blackhole gets smaller and smaller as it radiates and finally reduces to nothingness. Interesting fact: The intensity or energy of the radiation doesn't depend on the anything that was in the black hole. But this meant that the information of the things that were "sucked" into the blackhole was being lost, thus breaking a fundamental law of physics.
Soon, theoretical physicists studying string theory were looking at dualities in their equations, they found that when you take mathematical description of a system and add 1 spatial dimensions to it with a negative curvature, you get something similar to quantum fields in a three-dimensional universe without gravity. This is what made a principal called Holographic Principle, which states that: All information in 3 dimensional spaces can be "kept" and "held" on a 2 dimensional surface. Recall the event horizon of a black hole, it is 2 dimensional. It is the surface of a sphere. So basically this theory stated that the information of a black hole could actually be "stored" on the event horizon. Now, like you said, Hawking radiation happens because particles and anti particles pops in and out of existence. (They're NOT virtual particles) So when this happens at the event horizon, the anti-particles that fall into the black whole essentially "cancels out" the mass of the black hole, making the black hole smaller and smaller. And some of the information stored on the event horizon, gets released in the form of hawking radiation.
Stephen Hawking's paper on this is here
Nothing is "attracted" by anything in a blackhole. First off, how can something move or be attracted in a black hole? It has neither time, nor space. Spacetime gets distorted to the point you don't even know which is space and which is time. It's like the axis of a cartesian plane, an x-y graph, being scrunched up into a ball. How do you suppose the energies "attract" each other? Also, it is well known in the many-body scenario that depending on the arrangements of the bodys, the centre of attraction is different. By your criteria, I can make the singularity right next to an event horizon. Also, you got it the wrong way around. Relative to an observer inside the event horizon, there is a "singularity" which if he can see everything around him, that the matters surrounding him are moving towards. However, relative to an external observer, the dude never makes it pass the event horizon, he never crosses. This is why it is a deleted sequence from spacetime, because nothing makes pass it. They just stop at the event horizon, slowly turn red and vanish.abraker wrote:
Something to clear up. All the energy is being attracted to other energy inside the blackhole, which leads it all towards one point. However, since the energies are concentrated so much, they bend spacetime so much so that the energy as waves have to travel toward the one point indefinitely. Hence the singularity. Another thing, I would say that it's infinite density only relative to an observer outside the event horizon. Relative to an observer inside the event horizon, there is no such point. It's an infinite journey to the center, much like an infinite journey towards the edge of the universe.
If it gets redshifted, it is not getting sucked in. If it vanishes, it effectively does not cross the event horizon. The wave is not being stretched from the event horizon towards the singularity either, it is just that the geodesics of spacetime around that area means that the photons follow a curved path rather than a straight path to get to you, which means increasing the distance, and therefore redshifting. There are no parts of the wave being "stuck" on the event horizon, which means you will never observe that because that isn't true. Relative to an observer inside the event horizon, the wave does not get stretched either as they are in the same frame of reference, their geodesics are both twisted. In both cases, there are no "singularity".abraker wrote:
You see it redshifted as it is sucked in. It effectively crosses the event horizon. Though, the actual wave is being stretched from the event horizon to toward the singularity, so some part of the wave is indeed stuck on the event horizon. Time slows down indefinitely there, so the wave becomes highest freq gamma on the event horizon relative to an observer outside the event horizon, though you will never observer that. Relative to an observer inside the event horizon, the wave gets stretched indefinitely toward the "singularity" (which doesn't exist relative to there, just a direction) from an unreachable, external, source.
Yes....Because an empty universe expands..........................................abraker wrote:
This would be true if dark energy expands spacetime such that the cosmic microwave background gets redshifted slower than the massive blackhole's Hawking Radiation vaporizes it, allowing the blackhole to get larger as time goes on. Since dark energy seems to be accelerating the universe's expansion, I don't think this will be the case unless universal expansion decides to take another, slower, curve in the next trillion years or so.
my fucking god i wish people would just die
me too thankskai99 wrote:
my fucking god i wish people would just die
this is making me dyslexic