Question about infinite spaces and how higher/lower spaces relate

[Furudo_Erika]

I heard that all dimensional axes have to be infinite for a space to be "infinite".
But, I have a small problem with this. They shouldn't all need to be infinite to create an infinite space, and here is why:

Think of a hallway or corridor which doesn't have an end; an infinite corridor.
However, it has walls, a floor, and a ceiling; three meters each.
The walls represent width, the floor and ceiling represent height...and the corridor itself? It represents length.
So, the dimensions of the corridor is: ∞m, 3m, 3m...but it still has an infinite amount of 3D space inside it.

So according to this "infinite corridor", only one dimensional axis has to be infinite to equate an infinite higher-dimensional space, not all of them. This example having infinite length, but finite width and height, yet it still achieves an infinite 3D space/volume.

What about lower dimensional spaces? Same thing; (∞m, 3m) would still yield an infinitely stretching 2D space while being finite in height...but it is STILL an infinite 2D space as it still has an infinite 2D space. Not to mention the walls/floor/ceiling of the infinite corridor would also have infinite surface area as well.

Now, how does this relate to even higher-dimensional space?
If (∞m, 3m, 3m) equates to an infinite 3D space and (∞m, 3m) is an infinite 2D space...is (∞m, 3m, 3m, 3m) an infinite 4D space, and so on?

 

[DonkeySlayer06]

No axis going to infinity and all axis going to infinity are the same and both will not give an infinite volume because in the wall example you mentioned, Ceiling v Floor will not be as long as you hold 3 meters. if one axis of matter goes to infinity, it contains only one axis going to infinity, not all axes. . The same thing works in higher dimensions. In order to say Infinite Space, 3 axes of 3D Space are infinity, 4 axes in 4D Space, 5 axes in 5D Space, etc. In short, taking an axis to infinity does not mean infinite volume.

 

[Furudo_Erika]

No axis going to infinity and all axis going to infinity are the same and both will not give an infinite volume because in the wall example you mentioned, Ceiling v Floor will not be as long as you hold 3 meters. if one axis of matter goes to infinity, it contains only one axis going to infinity, not all axes. . The same thing works in higher dimensions. In order to say Infinite Space, 3 axes of 3D Space are infinity, 4 axes in 4D Space, 5 axes in 5D Space, etc. In short, taking an axis to infinity does not mean infinite volume.

Then what does ∞m x 3m x 3m equal?
It cannot be any finite value as multiplying infinity by anything is still infinity; infinite cubic meters; or infinite volume.
By that, it would still be infinite.

Say you have 1 m^3 blocks. Sure, you can only squeeze nine into the walls as that is 3m x 3m...but if you place those 9-block "layers" down the infinite corridor, you would have an infinite number of these block layers; meaning an infinite number of 1 m^3 blocks.
Which would be ∞ x 1 m^3 = ∞ m^3 as there is an infinite amount of 1 m^3 blocks that corridor can contain inside itself.
Like, no matter mow many block layers you place down the corridor, you can always add more. It would take an infinite amount of layers (and time) to fill it.

Simple geometry of a rectangular prism basically says that it would be infinite in volume, even if only length is infinite.

 

[Furudo_Erika]

No axis going to infinity and all axis going to infinity are the same and both will not give an infinite volume because in the wall example you mentioned, Ceiling v Floor will not be as long as you hold 3 meters. if one axis of matter goes to infinity, it contains only one axis going to infinity, not all axes. . The same thing works in higher dimensions. In order to say Infinite Space, 3 axes of 3D Space are infinity, 4 axes in 4D Space, 5 axes in 5D Space, etc. In short, taking an axis to infinity does not mean infinite volume.

Also, what about Low 2-C?
Which does not require a universe to have infinite physical space at all (it only has to be the size of the observable universe which is by no means infinite)

So unless Low 2-C is an exception for whatever reason with "all dimensional axes have to be infinite to qualify", then a lot of Low 2-Cs should not be Low 2-C unless proven that the spatial axes of the universe are all infinite.

As there is a lot of universes which have finite space (or at least not explicitly stated to be infinite, or even implied to be infinite), but are still Low 2-C despite not being infinite on every axis.

 

[Furudo_Erika]

Bump

 

[SeijiSetto]

taking an axis to infinity does not mean infinite volume.

you're wrong here and furudo's already explained why
∞ * 3 * 3 means the infinite corridor has infinite volume
so not all axes have to go to infinity to be an infinite volume

I heard that all dimensional axes have to be infinite for a space to be "infinite".
But, I have a small problem with this. They shouldn't all need to be infinite to create an infinite space, and here is why:

i have no clue if this is true
as far as i know (admittedly, not very far), until a recent revision, touhou's top tiers were Low 2-C because someone created an infinite corridor

 

[DonkeySlayer06]

Then what does ∞m x 3m x 3m equal?
It cannot be any finite value as multiplying infinity by anything is still infinity; infinite cubic meters; or infinite volume.
By that, it would still be infinite.

Say you have 1 m^3 blocks. Sure, you can only squeeze nine into the walls as that is 3m x 3m...but if you place those 9-block "layers" down the infinite corridor, you would have an infinite number of these block layers; meaning an infinite number of 1 m^3 blocks.
Which would be ∞ x 1 m^3 = ∞ m^3 as there is an infinite amount of 1 m^3 blocks that corridor can contain inside itself.
Like, no matter mow many block layers you place down the corridor, you can always add more. It would take an infinite amount of layers (and time) to fill it.

Simple geometry of a rectangular prism basically says that it would be infinite in volume, even if only length is infinite.

I understand what you mean, but it's not entirely correct. What we are trying to deal with as a subject here is the infinity of the Axes. If you keep the X of a room infinity, but the Y and Z of 3 meters, the area you will find is the infinite area of Y and Z bounded by 3 meters. It may seem like infinite space but in practice it is constrained in the Y and Z axes. If you think logically, a structure with infinite axes will contain a larger portion than the constrained one compared to Y and Z, since there is no restriction.

 

[DonkeySlayer06]

you're wrong here and furudo's already explained why
∞ * 3 * 3 means the infinite corridor has infinite volume
so not all axes have to go to infinity to be an infinite volume

i have no clue if this is true
as far as i know (admittedly, not very far), until a recent revision, touhou's top tiers were Low 2-C because someone created an infinite corridor

I have no idea about this subject. If I had seen Crt I would probably have refused

 

[SeijiSetto]

I have no idea about this subject. If I had seen Crt I would probably have refused

If you don't know, why did you answer as if you did?

 

[Furudo_Erika]

What you are talking about is "a space infinite in all directions".

But it terms of volume, a space infinite in all directions and a space infinite in only one both have the same volume mathematically:

Rectangular Prism:
∞m x 3m x 3m = ∞ m³

Cube:
∞m x ∞m x ∞m = ∞ m³

Or a sphere, which would have an infinite radius (and thus omnidirectionally infinite):
4/3 x π x ∞m³ = ∞ m³.

They all equal the same volume.
Regardless if only one dimensional axis is infinite, they all can still contain an infinite amount of volume;

A space infinite in all directions and a space infinite in only one direction both contain the same amount of available volumetric space.

 

[DonkeySlayer06]

If you don't know, why did you answer as if you did?

I'm talking about the character you call Touhoho creating an infinity corridor

 

[DonkeySlayer06]

What you are talking about is "a space infinite in all directions".

But it terms of volume, a space infinite in all directions and a space infinite in only one both have the same volume mathematically:

Rectangular Prism:
∞m x 3m x 3m = ∞ m³

Cube:
∞m x ∞m x ∞m = ∞ m³

Or a sphere, which would have an infinite radius (and thus omnidirectionally infinite):
4/3 x π x ∞m³ = ∞ m³.

They all equal the same volume.
Regardless if only one dimensional axis is infinite, they all can still contain an infinite amount of volume;

A space infinite in all directions and a space infinite in only one direction both contain the same amount of available volumetric space.

Look, they may all look the same on paper, but they really aren't. I can give you the following example about this. Consider that a corridor is infinitely long, but its height and depth are 3 meters, and the universe we are in is an infinite structure on every axis. The Corridor will be exactly the same on the X-axis of the Universe, but it does not have the same area and volume as the Universe, which is infinite on each axis, as Y and Z are still constrained to 3 meters. If you visualize this in your mind, you will know what I mean.

 

[Furudo_Erika]

Look, they may all look the same on paper, but they really aren't. I can give you the following example about this. Consider that a corridor is infinitely long, but its height and depth are 3 meters, and the universe we are in is an infinite structure on every axis. The Corridor will be exactly the same on the X-axis of the Universe, but it does not have the same area and volume as the Universe, which is infinite on each axis, as Y and Z are still constrained to 3 meters. If you visualize this in your mind, you will know what I mean.

And? It's still infinite volume nonetheless.

And even High 3-A can be reached by destroying an infinite amount of finite 3D spaces.

Characters or objects that demonstrate an infinite amount of energy on a 3-D scale, such as creating or destroying infinite mass, or those who can affect an infinite 3-D space. This extends to an infinite number of finite or infinite-sized 3-D universes or pocket dimensions when not accounting for when not accounting for any higher dimensions or time.

So even High 3-A explicitly stated that an infinite amount of finite 3D spaces is still High 3-A.

They DON'T have to all be infinite. In fact, none of them have to:
∞ x any finite-sized space = ∞ space according to High 3-A

Which the infinite corridor, again, can contain an infinite amount of 3D finite-sized spaces inside of it...which again, according to the literal tiering system, is High 3-A according to its qualifications.

So even if you destroy pocket dimensions that equate to, say 10 cubic meters.
If you destroy an infinite amount of those, it is still High 3-A as the total amount of space that would equate to is infinite.

 

[Iamunanimousinthat]

True. Even if a space had infinite dimensions, all those dimensions were finite, except one, it would still have infinite hypervolume.

 

[Furudo_Erika]

True. Even if a space had infinite dimensions, all those dimensions were finite, except one, it would still have infinite hypervolume.

Then...what tier would that be?
High 1-B, High 3-A, or Unknown?

High 1-B as it is hypervolume with infinite dimensional axes.

High 3-A as only one dimension is infinite (but it would still be hypervolume, infinite hypervolume in fact).

Unknown as, only one dimension is infinite, but all the rest is finite.

Actually the Unknown one brings me back to High 1-B. As the tiering system states that an infinite number of finite dimensional axes is listed as High 3-A, even though it still has hypervolume which cannot be fully affected with 3D attacks/range as only an infinitesimal 3D "slice" of that space would be affected.

 

[Iamunanimousinthat]

Then...what tier would that be?
High 1-B, High 3-A, or Unknown?

High 1-B as it is hypervolume with infinite dimensional axes.

High 3-A as only one dimension is infinite (but it would still be hypervolume, infinite hypervolume in fact).

Unknown as, only one dimension is infinite, but all the rest is finite.

Actually the Unknown one brings me back to High 1-B. As the tiering system states that an infinite number of finite dimensional axes is listed as High 3-A, even though it still has hypervolume which cannot be fully affected with 3D attacks/range.

It should be High-B because thats still infinite infinite-hypervolume

 

[Furudo_Erika]

It should be High-B because thats still infinite infinite-hypervolume

So...what about infinite-dimensional space that is finite on all axes?

As that was listed as High 3-A, but they would actually be functionally invulnerable to High 3-A attacks.

Since it takes an infinite amount of 3D "slices" in another dimension to create any kind of measurement in a higher-dimension. (n-spheres basically).

So a finite 4D volume has an infinite amount of 3D "slices", and a finite 5D volume would require an infinite amount of 4D "slices".

So by virtue of higher-dimensional physiology, a higher-dimensional being would see High 3-A as infinitesimal, regardless of how much hypervolume they have.

(Which is why an infinite number of finite higher-dimensional axes being tiered as High 3-A doesn't really sit right with me. As any finite-dimensional measurement would be infinitesimal to them)

 

[Furudo_Erika]

My personal opinion, which not a lot of people may agree with...

Is that higher-dimensional stuff, is range, and only range. Doesn't contribute to AP.

A bit of an extreme example...but picture this:

An aleph-omega amount of energy (which would be High 1-B in sheer cardinality) hitting a 4D being, but it only affects a three-dimensional slice of them.

Well, that 3D "slice" would most likely be completely decimated, but again...that 3D slice is nothing but an infinitesimal piece of their entire being. They would be virtually completely unharmed despite taking a High 1-B's amount of energy. In fact, they probably wouldn't even notice anything happened to them as that 3D "slice" is just that inconsequential.

And the reason? That High 1-B attack only covered a 3D "slice" of them, but it lacks the capability of going to the 4th-dimension and affecting that axis.

Which if it could, then that 4D being would be completely eradicated since High 1-B amounts of energy is being directed in all four dimensions rather than just three.

 

[Iamunanimousinthat]

So...what about infinite-dimensional space that is finite on all axes?

I think that is currently being discussed by staff.

Since it takes an infinite amount of 3D "slices" in another dimension to create any kind of measurement in a higher-dimension. (n-spheres basically).

Not true at all. You just need a new direction perpendicular to the third dimensions. You can keep stacking infinite upon finite 3D slices together and won’t make a 4D object unless they are oriented perpendicular to the third dimension.

So by virtue of higher-dimensional physiology, a higher-dimensional being would see High 3-A as infinitesimal, regardless of how much hypervolume they have.

Not true. They will see them as the size they are. Higher dimensional objects and beings still have the lower dimension embedded in them.

If a 3D sphere and a 4D sphere had the same radious, theyd be the same size in 3 dimensions. The 3D sphere would just be “flat” in the 4th dimension whole the other has depth. And the difference isn’t infinite, it would be proportional to the radius.

 

[Furudo_Erika]

I think that is currently being discussed by staff.



Not true at all. You just need a new direction perpendicular to the third dimensions. You can keep stacking infinite upon finite 3D slices together and won’t make a 4D object unless they are oriented perpendicular to the third dimension.



Not true. They will see them as the size they are. Higher dimensional objects and beings still have the lower dimension embedded in them.

If a 3D sphere and a 4D sphere had the same radious, theyd be the same size in 3 dimensions. The 3D sphere would just be “flat” in the 4th dimension whole the other has depth. And the difference isn’t infinite, it would be proportional to the radius.

I think you misinterpreted some of what I said.

The 3D slices do have to be oriented in the fourth dimension, but it takes an infinite amount of those slices in the fourth dimension to create any 4D measurement (or at the very least, I have always heard it took an infinite amount of slices from various sources. Even read from some staff messages saying it it took an infinite amount of slices for it. Like how a 1x1x1 3D cube is made of an infinite number of 1x1 2D squares all stacked in the third dimension)

 

[Iamunanimousinthat]

I think you misinterpreted some of what I said.

The 3D slices do have to be oriented in the fourth dimension, but it takes an infinite amount of those slices in the fourth dimension to create any 4D measurement (or at the very least, I have always heard it took an infinite amount of slices from various sources. Even read from some staff messages saying it it took an infinite amount of slices for it. Like how a 1x1x1 3D cube is made of an infinite number of 1x1 2D squares all stacked in the third dimension)

Those slices are infinitesmal and don’t add up to anything significant.

A 3 meter cylinder and a 300 meter cylinder (both with the same radius) have the same number of uncountably infinite 2D slices. And the slices are all the same size.

 

[Furudo_Erika]

Those slices are infinitesmal and don’t add up to anything significant.

A 3 meter cylinder and a 300 meter cylinder have the same number of uncountably infinite slices. And the slices all the same size.

And that's what I mean. Those slices are infinitesimal.

It doesn't matter how much power you put out, if all you affect is an infinitesimal 3D piece of something.
You must project it in the fourth dimension to truly affect its entire form rather than an infinitesimal slice of them.

Which is why I say higher-dimensional stuff is all range; how many axes you can project an attack rather than the sheer amount of power behind it.

At the very least, higher-dimensional physiology should grant some kind of invulnerability to attacks incapable of reaching all their dimensional axes, since it would just affect an infinitesimal slice of them.

I mean, what's gonna do more damage to a infinite-dimensional being?
Infinite energy on an infinitesimal 3D part of them, or a finite amount of energy projected among all of their dimensional axes (and thus affecting their entire being)?

This is especially relevant to higher-dimensional beings which tier does not correspond to their dimensionality. (As being higher-dimensional does not immediately grant you a higher tier). You could have 11-D physiology, but can still be 10-B for example.

 

[DonkeySlayer06]

And? It's still infinite volume nonetheless.

And even High 3-A can be reached by destroying an infinite amount of finite 3D spaces.

Characters or objects that demonstrate an infinite amount of energy on a 3-D scale, such as creating or destroying infinite mass, or those who can affect an infinite 3-D space. This extends to an infinite number of finite or infinite-sized 3-D universes or pocket dimensions when not accounting for when not accounting for any higher dimensions or time.

So even High 3-A explicitly stated that an infinite amount of finite 3D spaces is still High 3-A.

They DON'T have to all be infinite. In fact, none of them have to:
∞ x any finite-sized space = ∞ space according to High 3-A

Which the infinite corridor, again, can contain an infinite amount of 3D finite-sized spaces inside of it...which again, according to the literal tiering system, is High 3-A according to its qualifications.

So even if you destroy pocket dimensions that equate to, say 10 cubic meters.
If you destroy an infinite amount of those, it is still High 3-A as the total amount of space that would equate to is infinite.

I think the example I gave will suffice. The results of the equation are the same on paper, but never in reality. As I said, the example of an Infinite corridor and an Infinite universe is enough to understand this. Here's the example you gave. Can you fit a structure that is 6 meters long, height and depth into an infinite corridor of 3 meters Height and 3 meters Depth?

 

[DonkeySlayer06]

I reread Crt and realized I had misread it. What you want to ask is whether the structure of Infinite length but limited in height and depth is the same as an Infinite universe. Mathematically destroying both will give you H3A, but they are not the same in form. I apologize for my misunderstanding on this matter.

 

[Fixxed]

Well for get tier it must higher infinite, because we give a rating based on size. If it infinite 1D than it just 1D, you need a more bigger infinite for get higher tier. I mean we not use infinite of the lower dimension for be equal with the infinite in higher dimension or even any finite size

If it just have more complex of dimensionality, i think it just HDE. It why we have some human size character that are higher dimension

 

[Iamunanimousinthat]

Which is why I say higher-dimensional stuff is all range; how many axes you can project an attack rather than the sheer amount of power behind it.

Different sites view dimenisonal stuff differently. This site tiers it. It will be an uphill battle to have that changed.

At the very least, higher-dimensional physiology should grant some kind of invulnerability to attacks incapable of reaching all their dimensional axes, since it would just affect an infinitesimal slice of them.

Technically you wouldn't be affecting an infinitesimal slice of them. A 4D cube that has radius of 10 meters still has a 3D volume of 1000m^3 and a 3D surface area. . A 3D character would still be able to hit that, and the way energy works, the energy from their attack will still reach the 4D volume, even if said 3D character could not physically interact with it.

This is why characters do not get higher tiers for being higher dimensional. The tiers are more for destroying higher dimensional space.