How is destroying a spacetime continuum greater than destroying an infinite amount of 3-D universes?

[MightyFrogBeyond]

Low 2-C states destroying a STC is stronger than destroying an infinite amount of 3D universes.

My research finds an explanation: destroying a timeline ( assuming the attack is at least universal level ofc ),

means destroying the “infinite snapshots” a timeline has of a universe. These snapshots or rather seconds have their own infinite amount of smaller time frames, and those time frames have an infinite amount of smaller time frames of the universe too…
and that’s just one point on the timeline, there are infinite other points in a timeline that follow the sentence I mentioned earlier.
But all those time frames( snapshots), although they represent an infinite amount of infinite universes….
wouldn’t that still classify as being infinity?
Infinity X infinity= still infinity. And being low 2-C is being beyond infinite power, so…
how is destroying a timeline beyond infinite power?

 

[BestMGQScalerEver]

The snapshots are uncountably infinite rather than just countably infinite.

 

[MightyFrogBeyond]

The snapshots are uncountably infinite rather than just countably infinite.

The snapshots aren’t uncountably infinite.
The amount of them can go on forever but I can’t find a reason to assume that the amount “becomes uncountable”.

I’m sure I am wrong but I’m looking for a good explanation to my point that seemingly disproves a timeline not being uncountably infinite.

 

[MeidoIzayoi]

wouldn't an infinite amount of separate 3D universes or 3-A structures qualify for being a Low 2-C structure?

 

[KLOL506]

Spacetime is uncountable infinity because even a single point in time (No matter how big or how small) would contain an countably infinite number of 3D snapshots (Which would normally give us High 3-A without needing the space to be universal in size, but let Ultima cook first).

Given that time is infinite, infinite points in time sum up to... well, uncountable infinity. Hence, 4-D. The same logic applies for higher dimensions, uncountably infinite 4D snapshots lead to 5D, uncountably infinite 5D snapshots lead to 6D, so on and so forth.

 

[MightyFrogBeyond]

Uncountably long because even the smallest point in time would contain an countably infinite number of 3D snapshots (Which would normally give us High 3-A without needing the space to be universal in size, but let Ultima cook first).

Given that time is infinite, infinite points in time sum up to... well, uncountable infinity. Hence, 4-D.

That’s not how aleph one ( aka uncountable infinity ) works.
You can stack infinity upon infinity, raise it to the power of infinity; it still won’t reach aleph-1.
What you described would still be classified as countable, not uncountable.
( this is a reminder that I know I am wrong but I can’t find a convincing argument that disproves my claim ).

 

[Planck69]

wouldn't an infinite amount of separate 3D universes or 3-A structures qualify for being a Low 2-C structure?

No. It'd just be High 3-A.

A timeline works like a real number line. As in, since time is continuous, there are as many 3-dimensional snapshots of the universe as there are real numbers (like how there's infinite numbers between 1 and 2, infinite numbers between those numbers and so on). Due to how time acts the same way (you can subdivide 1 second infinitely, and subdivide those subdivisions infinitely, and so on).

I honestly dunno what's hard to fathom about this. It's like OP has a separate idea of uncountable infinity than what's used here or something.

 

[MightyFrogBeyond]

No. It'd just be High 3-A.

A timeline works like a real number line. As in, since time is continuous, there are as many 3-dimensional snapshots of the universe as there are real numbers (like how there's infinite numbers between 1 and 2, infinite numbers between those numbers and so on). Due to how time acts the same way (you can subdivide 1 second infinitely, and subdivide those subdivisions infinitely, and so on).

I honestly dunno what's hard to fathom about this. It's like OP has a separate idea of uncountable infinity than what's used here or something.

My understanding of aleph null and aleph one is consistent with this sub’s definition.

But, saying “there’s an infinite amount of numbers between 1 & 2, and an infinite amount of numbers between those numbers, ad infinitum” would simply mean that it’s just infinity^raised to infinity ^infinity ad infinitum.


And that’s not what aleph-1 is described as. It is beyond infinite.

Aleph null ( infinity ), represents infinity^infinity^infinity ad infinitum as well. Which is what a timeline is.

 

[Planck69]

I haven't mentioned either of those alephs, just the base logic that we use for why a timeline is Tier 2.

You can disagree with it but being blunt, this is a topic that's been done to death and I lack the energy to argue it for the umpteenth time.

 

[MightyFrogBeyond]

I haven't mentioned either of those alephs, just the base logic that we use for why a timeline is Tier 2.

You can disagree with it but being blunt, this is a topic that's been done to death and I lack the energy to argue it for the umpteenth time.

Please leave this thread open so others may be able to convince me.

 

[Planck69]

I'm not closing the thread, just pointing out that others may not care enough to do so.

 

[JustANormalPerson01]

But, saying “there’s an infinite amount of numbers between 1 & 2, and an infinite amount of numbers between those numbers, ad infinitum” would simply mean that it’s just infinity^raised to infinity ^infinity ad infinitum.

Not really. A set with cardinality of aleph 0 can have another number between each two numbers. Rational numbers is an example of that

And that’s not what aleph-1 is described as. It is beyond infinite.

Aleph 1 is not beyond infinite. Aleph 1 is a transfinite number, beyond aleph 0. But it is another infinity, not "beyond infinite"

Aleph null ( infinity ), represents infinity^infinity^infinity ad infinitum as well. Which is what a timeline is.

No. Aleph Null represents the cardinality of infinite sets that can be well-ordered.

Infinity^infinity^... ad infinitum is not aleph null. First of all, you must define what you mean by "infinity". Going by your comment, let's supose you mean Aleph 0.

Going by that assumption, 2^Aleph 0 is equal or greater than aleph 1. So, no, Aleph 0^Aleph 0^... ad infinitum is definitely not just Aleph 0

 

[MightyFrogBeyond]

Aleph null cannot equal to infinity^infinity^infinity?

What I understand is that, with the axiom of replacement, we can make bigger and bigger infinites than Aleph Null. As shown in this wiki recommended VSauce video( 18:40 ).


Maybe I’m misinterpreting what he says but I left assuming that since infinity accounts for all possible numbers and power sets, that infinity X infinity would still only equal infinity…
now I’m guessing infinity X infinity is a greater infinity than a normal infinity.

 

[JustANormalPerson01]

The existence of transfinite numbers between Aleph 0 and Aleph 1 is not –and most likely will never– be proven. It depends which branch of mathematics you're using, there is a transfinite number between Aleph 0 and Aleph 1.

Continuum Hypothesis and the Axiom of Choice, for example, state that there is no transfinite number between aleph 0 and aleph 1.

 

[TheGreatJedi13]

The snapshots aren’t uncountably infinite.
The amount of them can go on forever but I can’t find a reason to assume that the amount “becomes uncountable”.

I’m sure I am wrong but I’m looking for a good explanation to my point that seemingly disproves a timeline not being uncountably infinite.

imagine an infinite line and each 1cm or 1m of this line has infinite snapshots within them
by that logic it becomes
Infinity^infinity rather than infinity x infinity

because we already know there exists 1cm that is equivalent to an infinite snapshot
but that 1cm is infinitesimal compared to the infinite length of this line
making it that there is a power set of infinite in an infinite (∞x∞x∞x∞x∞x∞x...... so on) which makes a single set

in the end, if you take it too grounded it's just infinite
but if you consider infinite set theory and such it becomes a larger infinity which is where the aleph 0 aleph 1 comes in.

 

[MightyFrogBeyond]

imagine an infinite line and each 1cm or 1m of this line has infinite snapshots within them
by that logic it becomes
Infinity^infinity rather than infinity x infinity

because we already know there exists 1cm that is equivalent to an infinite snapshot
but that 1cm is infinitesimal compared to the infinite length of this line
making it that there is a power set of infinite in an infinite (∞x∞x∞x∞x∞x∞x...... so on) which makes a single set

in the end, if you take it too grounded it's just infinite
but if you consider infinite set theory and such it becomes a larger infinity which is where the aleph 0 aleph 1 comes in.

I have not considered infinite set theory, I’ll research more on that.

My confusion is coming from: if a character had infinite 3D power and a cosmology’s universe was the size of an infinite amount of universes, then that would mean they could also destroy the same amount of universes that a timeline contains. So, that would make infinite 3D power and destroying a timeline the same feat.
So, that’s why I’m having trouble seeing how destroying an timeline is a better feat than infinite 3D power.

 

[TheGreatJedi13]

I have not considered infinite set theory, I’ll research more on that.

My confusion is coming from: if a character had infinite 3D power and a cosmology’s universe was the size of an infinite amount of universes, then that would mean they could also destroy the same amount of universes that a timeline contains. So, that would make infinite 3D power and destroying a timeline the same feat.
So, that’s why I’m having trouble seeing how destroying an timeline is a better feat than infinite 3D power.

this usually because it is usually assumed that a timeline goes infinitely into the future
so like every 1 second becomes a set of infinite snapshots and there are infinite 1 seconds in an infinite timeline (I'm having a hard time visualizing this so I can't explain atm)

we assume the lowest infinity for infinite without elaboration so infinite 3D universe is aleph null
have an infinite set of them spread across a timeline that extends infinitely into the future
you get higher infinity

 

[MightyFrogBeyond]

we assume the lowest infinity for infinite without elaboration so infinite 3D universe is aleph null
have an infinite set of them spread across a timeline that extends infinitely into the future
you get higher infinity

That still sounds like infinity ^infinity. Even if infinity does go on forever, it still won’t reach aleph 1. But, I will assume that that’s how aleph 0 and 1 work in Set Theory.

I came up with my own explanation. Does this work?:

A timeline can only be measured with 4 coordinate axis, which means infinite 3D power can’t ever damage it since, infinite 3d power will always be bound to 3 dimension. This is why it’s more impressive to destroy a timeline, than an infinite amount of 3D universes.

 

[JustANormalPerson01]

I think that a timeline having uncountable infinite snapshots of 3D universe goes like this:

Let (x, y, z, t) be the coordinates of a point inside an universe, where x, y and z represent the 3 perpendicular directions of space and t represents the dimension of time.

All of those coordinates can take the value of any real number. Going to the concrete case of time: given any 3D space, t (time) can take the value of any real number to represent an instant of the timeline.

As we know, real numbers have the cardinality of aleph 1. Therefore, there are as many 3D snapshots within a timeline as numbers you can choose to represent the instant of time: aleph 1.

Let it be known that although this'd be mathematically correct for 4D vectorial spaces, I don't really know if there is some contradiction with time working like this, or if the tiering system does not follow this logic, but something else.

 

[TheGreatJedi13]

That still sounds like infinity ^infinity. Even if infinity does go on forever, it still won’t reach aleph 1. But, I will assume that that’s how aleph 0 and 1 work in Set Theory.

I came up with my own explanation. Does this work?:

A timeline can only be measured with 4 coordinate axis, which means infinite 3D power can’t ever damage it since, infinite 3d power will always be bound to 3 dimension. This is why it’s more impressive to destroy a timeline, than an infinite amount of 3D universes.

yes, you are correct.
i was mostly answering in math but yes if you add dimensional axis it becomes that
the 3D power may have the potency/mass or energy but without an axis to reach unreachable space/time it's not impressive nor as powerful

like infinite 3D universe would just be 1 line in comparison
while finite or infinite 3D space with spacetime would be a square

 

[GreatIskandar14045]

You can stack infinity upon infinity, raise it to the power of infinity; it still won’t reach aleph-1.

That's not true.

Infinite^infinite is equal to beth-1, which is equal to R or 1 dimension (which is aleph-1 equivalent in this site's standards). I can go on and explain why aleph-1 might be smaller than R, but that would be derailing.

A spacetime continuum can be represented as 1 dimension (length) containing an uncountable amount of 0 dimension (point)—infinite points make up length. Think about the length as time and the points as space; then you have a spacetime continuum.

So you are now comparing infinite 3D universes and uncountably infinite 3D universes; the latter is superior.

 

[MightyFrogBeyond]

That's not true.

Infinite^infinite is equal to beth-1, which is equal to R or 1 dimension (which is aleph-1 equivalent in this site's standards). I can go on and explain why aleph-1 might be smaller than R, but that would be derailing.

But the VSauce video proves you wrong, no?
VSauce says infinity^infinity^infinity^ etc., cannot equal Aleph 1.

In 18:05, he shows how aleph raised to omega^omega^omega, would still come before Aleph 1.

 

[GreatIskandar14045]

But the VSauce video proves you wrong, no?
VSauce says infinity^infinity^infinity^ etc., cannot equal Aleph 1.

In 18:05, he shows how aleph raised to omega^omega^omega, would still come before Aleph 1.

Trust me, I'm aware of that video. VSauce talks about ordinal numbers, not cardinal numbers (it's omega, not aleph). In ordinality, you won't reach higher infinity by using infinite^infinite^infinite, and so on. But in cardinal numbers, it does.

This site's tiering system uses cardinality because it's more relevant to size; cardinal is about how we count things, while ordinal is about rank or how we arrange things.

 

[MightyFrogBeyond]

This site's tiering system uses cardinality because it's more relevant to size; cardinal is about how we count things, while ordinal is about rank or how we arrange things.

Are there any differences on how VSBW uses cardinality? Like, is it the same as how scientists use it?

Also, have you seen my timeline being a 4 dimensional construct comment? It’s number 18. Do you agree with that explanation? I want to use that explanation for why destroying a timeline is more impressive than destroying, an infinite amount of 3d universes.

 

[ProfectusInfinity]

I came up with my own explanation. Does this work?:

A timeline can only be measured with 4 coordinate axis, which means infinite 3D power can’t ever damage it since, infinite 3d power will always be bound to 3 dimension. This is why it’s more impressive to destroy a timeline, than an infinite amount of 3D universes.

This alternate explanation isn't very good. It practically boils down to "Time is a higher infinity for the sole reason that it's 4-D," which doesn't work as an explanation since the first few paragraphs of the tiering system FAQ straight up explain why higher dimensions aren't automatically higher infinities.

I agree with some of the other people here that your contentions seem to lie in an irregular understanding of cardinality.

 

[MightyFrogBeyond]

This alternate explanation isn't very good. It practically boils down to "Time is a higher infinity for the sole reason that it's 4-D," which doesn't work as an explanation since the first few paragraphs of the tiering system FAQ straight up explain why higher dimensions aren't automatically higher infinities.

I agree with some of the other people here that your contentions seem to lie in an irregular understanding of cardinality.

I thought I had a pretty good understanding after watching the VSauce video?

I’ll try another approach, maybe it’ll help explain my thought process.

Saga 1: My character has an infinite amount of 3D power.
Saga 2: My character has an infinite X infinite X infinite^ infinite ( etc. ), amount of 3D power.
Saga 3: My character has 4D power. Which means no amount of 3D power can ever reach 4D power. Or, would this be 4DSTC continuum power? Because, I want my character to be able to destroy time at a universal scale and also be able to affect 4D objects such as a 4D tree, 4D water, 4D cars etc.



Do you see now? I want saga 2 to be a “break” between infinite 3D power and 4D power. And, using ordinals is the best way to do that.
But, as I have mentioned, I can’t see how destroying a timeline is different than destroying an infinite^infinite amount of universes.
My only explanation for a difference would be that a timeline is a 4D construct which automatically makes it better than infinite X infinite 3D power.

 

[ProfectusInfinity]

Saga 3: My character has 4D power. Which means no amount of 3D power can ever reach 4D power. Or, would this be 4DSTC continuum power? Because, I want my character to be able to destroy time at a universal scale and also be able to affect 4D objects such as a 4D tree, 4D water, 4D cars etc.

My only explanation for a difference would be that a timeline is a 4D construct which automatically makes it better than infinite X infinite 3D power.

As I said before, according to the tiering system FAQ, it doesn't work this way.

Q: When are higher dimensions not viable to use as evidence for Tier 2 and above?​

A: Whether higher-dimensional entities qualify for such high tiers or not depends on several different factors, which may take root both in and out-of-verse. To explain this situation, we must first clarify what exactly being higher-dimensional entails.

Are higher-dimensional beings infinitely larger than lower-dimensional equivalents?​

In a way, yes, though not how most would think when using this word. Basically, an arbitrary object of dimension n is essentially comprised by the total sum of uncountably infinite objects of one dimension less, which may be described as lower-dimensional "slices", each corresponding to one of the infinite points of a line. For instance, a square is made of infinitely many line segments (Lined up on the y-axis), a cube of infinitely many squares (Lined up on the z-axis), and so on.

One may think of it as a multiplication between sets: For instance, the unit square [0,1]² may be expressed as the product of two unit intervals [0,1] x [0,1], which itself can be visualized as taking "copies" of the first interval and lining them up along each point of the second interval, of which there are uncountably infinitely-many, thus forming a square out of infinite line segments.

Are higher-dimensional beings infinitely stronger than lower-dimensional equivalents?​

Unintuitive as that may be: Not necessarily, as a number of characteristics through which we quantify the strength or power of a character can remain unchanged when transitioning between higher and lower dimensions. For example: Mass is a quantity that is detached from the dimension of the object which it is inherent to, and unlike volume is not divided in units corresponding to each particular dimension (1-volume [length], 2-volume [area], 3-volume, 4-volume...). It is singular in nature and its units equally apply to all dimensions; whether it is distributed over an area or a volume only tells us about the span of space in which it is spread, not about the quantity itself.

As a consequence of that, much of the calculation methods which are used to measure strength apply equally to both higher and lower dimensions, as they do not care about the extra variables and often work with a single one of them. Examples of this are kinetic energy (Ek=0.5*M*V^2), force (F=M*A), work (W=F*d), and etc.

An intuitive example of that is found in the general definition of Work as defined in physics: In essence, as work itself denotes the energy applied to an object as it is displaced along a given path, the basic formula for calculating it only takes into account a single variable, and the path itself is treated as an one-dimensional object, regardless of the dimension of the space in which the action itself takes place.

Hence, a higher-dimensional entity can be both stronger or weaker than a lower-dimensional one, and thus, they are usually quantified based on their own feats, instead of dimensionality alone. If a character is merely stated to be higher-dimensional and simultaneously has no other feats to derive anything noteworthy from, then they are put at Unknown, and the same applies to lower dimensions as well.

Do note, however, that them not qualifying for Tier 2 and above doesn't mean they are "fake" higher-dimensional beings or anything of the sort. It is simply that being higher-dimensional does not inherently mean they have infinite power in the first place, as explained above.

Q: When are higher dimensions valid, then?​

A: One of the more straightforward ways to qualify for Tier 2 and up through higher dimensions is by affecting whole higher-dimensional universes which can embed the whole of lower-dimensional ones within themselves. For example: A cosmology where the entirety of our 3-dimensional universe is in fact a subset of a much greater 4-dimensional space, or generalizations of this same scenario to higher numbers of dimensions; i.e A cosmology where the four-dimensional spacetime continuum is just the infinitesimal surface of a 5-dimensional object, and etc.

However, vaguer cases where a universe is merely stated to be higher-dimensional while existing in a scaling vacuum with no previously established relationship of superiority towards lower-dimensional ones (or no evidence to infer such a relationship from) should be analysed more carefully. In such cases where information as to their exact nature and scale is scarce, it is preferable that the higher dimensions in question be fully-sized in order to qualify.

Furthermore, higher-dimensional entities can also qualify for higher tiers when the verse which they are from explicitly defines them as being infinitely above lower-dimensional ones in power and/or existential status. An example of this being verses such as Umineko no Naku Koro ni. However, lower-dimensional beings being stated to be "flat" in comparison to higher-dimensional aliens is not necessarily grounds for assuming the latter has infinitely more power (For reasons outlined in the answer above), and thus, such scenarios must also be analyzed case-by-case.

Higher dimensions are infinitely larger than low dimensions in the loose sense that they comprise uncountably infinitely many "slices" of lower dimensions. For example, set 1 [0,5] could represent one axis, and set 2 [0,5] could represent another. Constructing a higher dimensional 2-D object from these sets would require you to find a cartesian product. The X axis would be a set of points from 0 to 5, and the Y axis would a set of points from 0 to 5, which when graphed, gives you a 5 by 5 square. Creating this square is like taking a line of the points from 0 to 5 of either axis, then using the other axis as the direction along which uncountably infinitely many of such lines are aligned. In other words, a 5 by 5 square is like uncountably infinitely many vertical lines associated with each real interval of a horizontal axis.

However, this doesn't mean that higher dimensions are infinitely stronger than lower ones. This is because the parameters we use to determine power levels like mass and energy are scalar quantities, which means they're not limited or contrained to a value for displacement or direction: they have no dimensioned value, and can be applied and permeate through all spatial dimensional axes.

This is why higher dimensions need to be significantly larger than lower ones to be considered "higher levels of infinity" based on the tiering system FAQ.

Time being 4-D doesn't render it "automatically" better than any countably infinity extension of 3-D power. An 11-D object that can be modeled as a real coordinate space like [R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R] or R^11 is indeed, 11 levels of infinity. On the other hand, an 11-D object that is a cartesian product of countable sets like [4][4]x[4]x[4]x[4]x[4]x[4]x[4]x[4]x[4]x[4] would give you some random finite value. You said "able to affect 4-D objects" as if being higher dimensional makes on object infinitely more durable, which isn't remotely true. The finite 11-D object I introduced, could be fodderized easily by significant 3-D power (R^3).

 

[JustANormalPerson01]

[0, 4] is not a countable set

 

[JustANormalPerson01]

Now that you corrected it, what you've given is just a point of coordinates (4, ..., 4), not a 11-D object.

The reason why higher dimensions do not give higher tier by default is not because of the direct product of sets, but because the unity of energy (Joules) does not depend of the dimension we're talking about. Any higher dimensional object can be divided into uncountable infinite lower dimensional "slices", you just need to do the intersection of said object with each a lower dimensional plane/hyperplane.

 

[MightyFrogBeyond]

As I said before, according to the tiering system FAQ, it doesn't work this way.

Higher dimensions are infinitely larger than low dimensions in the loose sense that they comprise uncountably infinitely many "slices" of lower dimensions. For example, set 1 [0,5] could represent one axis, and set 2 [0,5] could represent another. Constructing a higher dimensional 2-D object from these sets would require you to find a cartesian product. The X axis would be a set of points from 0 to 5, and the Y axis would a set of points from 0 to 5, which when graphed, gives you a 5 by 5 square. Creating this square is like taking a line of the points from 0 to 5 of either axis, then using the other axis as the direction along which uncountably infinitely many of such lines are aligned. In other words, a 5 by 5 square is like uncountably infinitely many vertical lines associated with each real interval of a horizontal axis.

However, this doesn't mean that higher dimensions are infinitely stronger than lower ones. This is because the parameters we use to determine power levels like mass and energy are scalar quantities, which means they're not limited or contrained to a value for displacement or direction: they have no dimensioned value, and can be applied and permeate through all spatial dimensional axes.

This is why higher dimensions need to be significantly larger than lower ones to be considered "higher levels of infinity" based on the tiering system FAQ.

Time being 4-D doesn't render it "automatically" better than any countably infinity extension of 3-D power. An 11-D object that can be modeled as a real coordinate space like [R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R]x[R] or R^11 is indeed, 11 levels of infinity. On the other hand, an 11-D object that is a cartesian product of countable sets like [4][4]x[4]x[4]x[4]x[4]x[4]x[4]x[4]x[4]x[4] would give you some random finite value. You said "able to affect 4-D objects" as if being higher dimensional makes on object infinitely more durable, which isn't remotely true. The finite 11-D object I introduced, could be fodderized easily by significant 3-D power (R^3).

I’m seeing a lot of terminology and examples I’m not understanding. There has to be a more simpler explanation.

what I did understand is that:
-an object with an extra coordinate axis dimension doesn’t make it uncountably more infinitely durable than a character bound by only 3 coordinate axis.
- I now know a 4d space can contain an uncountably infinite amount of 3d mass.

Could you rephrase the x and y axis of your square example? I understand you can make a 2D square with those 2 sets if you let them represent an x and y axis.

But, you lost me when you started talking about how when you use a Cartesian product to make a new axis, it is used as a direction for one of the x or y axis to be aligned an uncountably infinite amount of times? Also how they’re associated with the horizontal axis confuses me.
Perhaps a picture would help?

 

[ProfectusInfinity]

I’m seeing a lot of terminology and examples I’m not understanding. There has to be a more simpler explanation.

what I did understand is that:
-an object with an extra coordinate axis dimension doesn’t make it uncountably more infinitely durable than a character bound by only 3 coordinate axis.
- I now know a 4d space can contain an uncountably infinite amount of 3d mass.

Could you rephrase the x and y axis of your square example? I understand you can make a 2D square with those 2 sets if you let them represent an x and y axis.

But, you lost me when you started talking about how when you use a Cartesian product to make a new axis, it is used as a direction for one of the x or y axis to be aligned an uncountably infinite amount of times? Also how they’re associated with the horizontal axis confuses me.
Perhaps a picture would help?

The cartesian product is a kind of multiplication in set theory that returns a set from multiple sets by considering all possible combinations of elements. In other words, it combines every element from one set with every element from another set.

Let's consider two sets, A and B:

A = {1, 2} B = {x, y}

The Cartesian product of A and B, denoted as A × B, would be:

A × B = {(1, x), (1, y), (2, x), (2, y)}

Each element in the resulting set is an ordered pair, where the first element is from set A and the second element is from set B. In this example, the Cartesian product represents all possible combinations of elements between the sets A and B.

So, A × B is {(1, x), (1, y), (2, x), (2, y)}.

You asked me to provide a visual. First off, note that my square example is meant to illustrate this particular section of the FAQ:

Are higher-dimensional beings infinitely larger than lower-dimensional equivalents?​

In a way, yes, though not how most would think when using this word. Basically, an arbitrary object of dimension n is essentially comprised by the total sum of uncountably infinite objects of one dimension less, which may be described as lower-dimensional "slices", each corresponding to one of the infinite points of a line. For instance, a square is made of infinitely many line segments (Lined up on the y-axis), a cube of infinitely many squares (Lined up on the z-axis), and so on.

One may think of it as a multiplication between sets: For instance, the unit square [0,1]² may be expressed as the product of two unit intervals [0,1] x [0,1], which itself can be visualized as taking "copies" of the first interval and lining them up along each point of the second interval, of which there are uncountably infinitely-many, thus forming a square out of infinite line segments.

Ultima explained something like this regarding using different sets to represent different axes, so I'm mostly referencing him.

As I said before, an X axis could be the set of all points from 0 to 5. The Y axis could also be the set of all points from 0 to 5. The basic construction of a space with n dimensions is a Cartesian Product, A x B, which is basically just taking all of B and attaching a copy of it to each point of A.

In this case, creating a 2-dimensional square means taking the cartesian product of [0,5]: a set of numbers including values of and between 0 and 5, and [0,5]: another set of numbers including the values of and between 0 and 5. Let's say one [0,5] in isolation, was a horizontal line 5-units long: the X-axis. By creating this square, you're attaching such a line to every point along the Y-axis from 0 to 5, making that square equivalent to uncountably infinitely many horizontal lines.

Did I explain it right this time (I'm admittedly an amatuer at the set theory aspect of the tiering system, but I'm trying)?

 

[MightyFrogBeyond]

The cartesian product is a kind of multiplication in set theory that returns a set from multiple sets by considering all possible combinations of elements. In other words, it combines every element from one set with every element from another set.

Let's consider two sets, A and B:

A = {1, 2} B = {x, y}

The Cartesian product of A and B, denoted as A × B, would be:

A × B = {(1, x), (1, y), (2, x), (2, y)}

Each element in the resulting set is an ordered pair, where the first element is from set A and the second element is from set B. In this example, the Cartesian product represents all possible combinations of elements between the sets A and B.

So, A × B is {(1, x), (1, y), (2, x), (2, y)}.

You asked me to provide a visual. First off, note that my square example is meant to illustrate this particular section of the FAQ:

Ultima explained something like this regarding using different sets to represent different axes, so I'm mostly referencing him.

As I said before, an X axis could be the set of all points from 0 to 5. The Y axis could also be the set of all points from 0 to 5. The basic construction of a space with n dimensions is a Cartesian Product, A x B, which is basically just taking all of B and attaching a copy of it to each point of A.

In this case, creating a 2-dimensional square means taking the cartesian product of [0,5]: a set of numbers including values of and between 0 and 5, and [0,5]: another set of numbers including the values of and between 0 and 5. Let's say one [0,5] in isolation, was a horizontal line 5-units long: the X-axis. By creating this square, you're attaching such a line to every point along the Y-axis from 0 to 5, making that square equivalent to uncountably infinitely many horizontal lines.

Did I explain it right this time (I'm admittedly an amatuer at the set theory aspect of the tiering system, but I'm trying)?

You did a very good job simplifying it, thank you.
: Imagine 2 sets with 5 elements each.
: the Cartesian product multiplies those 2 set’s elements to, create all possible combintations.
: creating a 2D square, in other words: is just the cartesian product of a X-axis set, and a Y-axis set.
: I understand we’re connecting each X-axis’s element to the element that belongs in the Y-axis.
: I don’t see how connecting those 2 sets makes the square uncountably infinitely many horizantal lines. I’m lost.

Does it have something to do with how a 2D square can contain an uncountably infinite amount of 1D vertical lines?

 

[JustANormalPerson01]

You did a very good job simplifying it, thank you.
: Imagine 2 sets with 5 elements each.
: the Cartesian product multiplies those 2 set’s elements to, create all possible combintations.
: creating a 2D square,

The cartesian product of 2 sets with 5 elements each would not create a square, but 25 different points. For example, let A={1, 2, 3, 4, 5}

AxA={(1,1),(1,2),(1,3),(1,4),(1,5),...,(5,5)}

That is not a square

I don’t see how connecting those 2 sets makes the square uncountably infinitely many horizantal lines. I’m lost.

Think of the square formed by the direct product of [0, 1]x[0, 1]

From there, you can take the line which goes from (0, 0) to (0, 1)

But you could also take the line which goes from (0.3, 0) to (0.3, 1), or the line which goes from (0.137461616361, 0) to (0.137461616361, 1), etc. How many lines can you get? As much as real numbers are between 0 and 1: uncountable infinite numbers.

 

[MightyFrogBeyond]

The cartesian product of 2 sets with 5 elements each would not create a square, but 25 different points. For example, let A={1, 2, 3, 4, 5}

AxA={(1,1),(1,2),(1,3),(1,4),(1,5),...,(5,5)}

That is not a square

Think of the square formed by the direct product of [0, 1]x[0, 1]

From there, you can take the line which goes from (0, 0) to (0, 1)

But you could also take the line which goes from (0.3, 0) to (0.3, 1), or the line which goes from (0.137461616361, 0) to (0.137461616361, 1), etc. How many lines can you get? As much as real numbers are between 0 and 1: uncountable infinite numbers.

I see. And, the amount of sets we can make is uncountable because we can make an infinity out of ( 0.111, 0 ), and another infinity out of ( 0.1211, 0 ), and another infinity out of ( 0.1311, 0 ) etc.

So, i looked up this video and I think I understand what uncountable infinity is now.


So, back to Low 2-C because I think I’m starting to understand.

If you destroy a timeline, you’re not just destroying between 1 and 2 seconds but, everything possible in between. And everything in between 1 and 2 is an uncountable amount right? Because there’s real numbers inside those 2 numbers right?
I’m basing this off of comment # 7.

 

[ProfectusInfinity]

If you destroy a timeline, you’re not just destroying between 1 and 2 seconds but, everything possible in between. And everything in between 1 and 2 is an uncountable amount right? Because there’s real numbers inside those 2 numbers right?
I’m basing this off of comment # 7.

Exactly, I think you get the gist now.

 

[MightyFrogBeyond]

Exactly, I think you get the gist now.

When a timeline is destroyed, if each 2 seconds can contain an uncountable amount of universes

and since there are more than just 2 seconds in a timeline ( obviously ),

wouldn’t we be destroying more than one uncountable amount of universes?


How many universes are destroyed when destroying a timeline ? An uncountably uncountable amount of universes?

 

[JustANormalPerson01]

The amount of real numbers between 0 and 1 are the same as the amount of all real numbers

Regarding destroying just 2 seconds within a timeline, I think there is a standard which says it is not Low 2-C. Don't know the reason, though

 

[Planck69]

The amount of real numbers between 0 and 1 are the same as the amount of all real numbers

Regarding destroying just 2 seconds within a timeline, I think there is a standard which says it is not Low 2-C. Don't know the reason, though

Our High 3-A/Low 2-C border is generally weird about that, yeah. It's technically also Tier 2 but isn't considered that currently.