Acceptable Narrative Examples of "Uncountably Infinite" Addition to the Tiering System Explanation Page

[Firestorm808]

Within our tiering system, we have used the phrase multiple times.

"Being “infinitely” stronger than this level, unless uncountably so, does not qualify for any higher tier."

"An uncountably infinite number, assumed to be the cardinality of the real numbers themselves"

"such exceed any possible number of levels contained in the previous tiers, including an infinite or uncountably infinite number."

"even an infinite or uncountably amount of such levels."

I understand that our Tiering Explanation Page explains using cardinals and mathematics. However, I'm sure some users, including myself, can find these mathematical concepts confusing when analyzing a narrative.

It's uncommon for traditional media to use explicit terms like "Uncountably Infinite," "Cardinals," and "Alephs." However, some franchises are able to convey the same meaning in other ways.

With that in mind, I hope we can compile common examples that our users can use as a reference or a starting point when analyzing narratives in the future.

 

[KLOL506]

I think in my personal opinion this should all be case-by-case.

@DontTalkDT @Executor_N0 @Ultima_Reality @Planck69 @Theglassman12 @Emirp sumitpo @AbaddonTheDisappointment @DarkDragonMedeus @Elizhaa @LordGriffin1000 @Maverick_Zero_X @Starter_Pack @Dereck03 @DarkGrath @Sir_Ovens @ByAsura

 

[DarkDragonMedeus]

Yeah, this is case by case. Definitions are definitions, but the real debate is knowing when it is appropriate to differentiate the difference between context making statements literal and acknowledging that they're commonly used as hyperboles.

 

[Firestorm808]

I understand that a proper analysis is case by case. However, a starting point and reference for what contexts to look for would be beneficial.

 

[KLOL506]

Again, I believe one starting point that may work for one verse may not be so useful for the other, especially with regards to Tier 1 and such.

 

[Firestorm808]

Again, I believe one starting point that may work for one verse may not be so useful for the other, especially with regards to Tier 1 and such.

It's moreso how you portray the quantity of "uncountable" rather than any specific tiering.

 

[KLOL506]

It's moreso how you portray the quantity of "uncountable" rather than any specific tiering.

Even so, one verse's subtle definition of "uncountable" may not necessarily work for the other.

 

[Firestorm808]

Even so, one verse's subtle definition of "uncountable" may not necessarily work for the other.

Aren't the narratives supposed to be evaluated based on the site's definition of uncountable, not the franchise's?

In turn, we would supplement a sample narrative that meets our site's definition.

 

[Fixxed]

Bump

 

[Antvasima]

@AKM sama @DontTalkDT @DarkDragonMedeus @Mr._Bambu @Celestial_Pegasus @Wokistan @Ultima_Reality @Elizhaa @Qawsedf234 @ByAsura @Sir_Ovens @Damage3245 @Starter_Pack @Abstractions @LordGriffin1000 @Colonel_Krukov @SamanPatou @GyroNutz @Firestorm808 @Everything12 @Maverick_Zero_X @Crabwhale @Agnaa @Just_a_Random_Butler @DarkGrath @Dereck03 @Eficiente @Planck69 @Deagonx

 

[KLOL506]

@AKM sama @DontTalkDT @DarkDragonMedeus @Mr._Bambu @Celestial_Pegasus @Wokistan @Ultima_Reality @Elizhaa @Qawsedf234 @ByAsura @Sir_Ovens @Damage3245 @Starter_Pack @Abstractions @LordGriffin1000 @Colonel_Krukov @SamanPatou @GyroNutz @Firestorm808 @Everything12 @Maverick_Zero_X @Crabwhale @Agnaa @Just_a_Random_Butler @DarkGrath @Dereck03 @Eficiente @Planck69 @Deagonx

There are a lot of people in this list who would rather not be bothered by this, since they more or less can't stand Tier 1.

Also AFAIK, DT won't be available for a month or two, and Ultima seems to be uh... busy. That and I've already tagged a bunch of the staff in that list prior.

 

[Antvasima]

Okay. My apologies about that then, but it is very hard for me to keep track of all the personal preferences of our around 80 staff members.

 

[LordGriffin1000]

Sadly, all the verses I'm knowledgeable on (even the ones that reach multiversal in scope) don't use "uncountable infinite" or those other terms so I can't provide any examples.

 

[IdiosyncraticLawyer]

Bump.

 

[Antvasima]

@Celestial_Pegasus @Wokistan @Ultima_Reality @Elizhaa @Qawsedf234 @ByAsura @Sir_Ovens @Damage3245 @Starter_Pack @Abstractions @Colonel_Krukov @SamanPatou @GyroNutz @Everything12 @Maverick_Zero_X @Crabwhale @Agnaa @DarkGrath @Planck69

Would any of you be willing to help out with evaluating this please?

 

[Qawsedf234]

Would any of you be willing to help out with evaluating this please?

I'll wing it I guess

"Being “infinitely” stronger than this level, unless uncountably so, does not qualify for any higher tier."

The easiest way to show this would be an exponential slope gif and to use a meme version of that Saitama vs God:

Basically an infinite increase would never reach a true or higher level of infinity. The gap would is "inaccessible".

"An uncountably infinite number, assumed to be the cardinality of the real numbers themselves"

A cardinal number is a set of numbers. For example Aleph-0 is an infinite set of any of the following:

• the set of natural numbers, irrespective of including or excluding zero,
• the set of all integers,
• any infinite subset of the integers, such as the set of all square numbers or the set of all prime numbers,
• the set of all rational numbers,
• the set of all constructible numbers (in the geometric sense),
• the set of all algebraic numbers,
• the set of all computable numbers,
• the set of all computable functions,
• the set of all binary strings of finite length, and
• the set of all finite subsets of any given countably infinite set.

While Aleph-1 is a cardinal set of all cardinal sets. So its an infinite arrangements of an infinite amount of Aleph-0 arrangements. In the same fashion Aleph-2 is an infinite arrangement of all Aleph-1 arrangements

"such exceed any possible number of levels contained in the previous tiers, including an infinite or uncountably infinite number."

See above. But afaik its just that because you have an infinite number of set arrangements, being uncountably infinite higher still wouldn't account for the arrangements of all sets but just any singular set of any of those sets.

 

[Everything12]

As one of the few pro-Tier 1 staff members, I have absolutely no good examples that would help explain this off the top of my head.

 

[Qawsedf234]

As one of the few pro-Tier 1 staff members, I have absolutely no good examples that would help explain this off the top of my head.

We could use the Von Neumann universe example since it involves sets:

 

[Everything12]

That isn't really to help explain anything to anyone who doesn't already understand it.

Actually, I just had a thought based off what I just commented on in my own CRT.

Zeno's paradox, while not an actual thing in reality is a way to talk about the Real Numbers, and Gojo and his ability is quite popular with even the mainstream audience. Most people probably don't accurately understand how Infinity works but it would be a good starting point to explain it.

 

[Qawsedf234]

Zeno's paradox, while not an actual thing in reality is a way to talk about the Real Numbers, and Gojo and his ability is quite popular with even the mainstream audience. Most people probably don't accurately understand how Infinity works but it would be a good starting point to explain it.

Yeah those are probably easier to digest.

 

[Antvasima]

Thank you very much for helping out, @Qawsedf234 .

@Ultima_Reality @DontTalkDT

Do you find his suggested solution acceptable?

 

[Fixxed]

Bump

 

[Antvasima]

Does this apply here?

https://vsbattles.com/threads/uncou...me-qualitative-statement.167959/#post-6541032

 

[Firestorm808]

Does this apply here?

https://vsbattles.com/threads/uncou...me-qualitative-statement.167959/#post-6541032

Yes. Ideally we want some sample narratives statements that convey the same concept outside of direct mathematical verbiage.

 

[Antvasima]

@Ultima_Reality

What do you think about this?

 

[IdiosyncraticLawyer]

Bump.

 

[Antvasima]

@Ultima_Reality

We need some input here.

 

[Firestorm808]

Bump.

 

[Firestorm808]

@Qawsedf234

We also have the following description:

Low 1-C with universes involves an uncountable infinite set or Aleph-1. An Aleph-1 set is an infinite set composed of all infinite variations of something inside of it. So, in this case, it can never be reached by an infinite amount of universes. It can't even be reached by an infinite amount of universes branched from universes. It has to be an infinite array of 2-A spaces with universes. For your hypothetical example, if you have an infinite number of points that can branch into an infinite number of different space-times, there is a good argument to be made for Low 1-C.

So, to use a practical example, we have the following parameters:

1. We have an infinitely long timeline (A)
2. (A) has an infinite number of branch points ( n )
3. Each of those branches is a timeline with an infinite number of branches. (n^n)

The above differs from the common narrative description of a timeline that branches infinitely.

Is that correct?

 

[Qawsedf234]

The above differs from the common narrative description of a timeline that branches infinitely.

Is that correct?

I believe so, since a timeline is generally just an uncountable infinite nu.mber of 3-A snapshots. Without a second temporal axis, the only consistent way I see replicating such a thing is a recursive amount of 2-A space stacked together.

 

[Firestorm808]

I believe so, since a timeline is generally just an uncountable infinite nu.mber of 3-A snapshots. Without a second temporal axis, the only consistent way I see replicating such a thing is a recursive amount of 2-A space stacked together.

To clarify, we are defining the "common narrative description of a timeline that branches infinitely" as one set of 2-A and not a recursive one.

A narrative description of recursion would lead to uncountable amount.

If I understand the methodology correctly, are we accepting the Many Worlds interpretation (where every quantum event is a branch point) as a practical example of "Uncountable," or is it a different metaphysics hypothesis?

 

[Qawsedf234]

To clarify, we are defining the "common narrative description of a timeline that branches infinitely" as one set of 2-A

Yes. Because the example given is a 2-A structure that branches infinitely and who's branched paths also branch infinitely. A timeline branching infinitely by itself is just 2-A and nothing more.

If I understand the methodology correctly, are we accepting the Many Worlds interpretation (where every quantum event is a branch point) as a practical example of "Uncountable," or is it a different metaphysics hypothesis?

I don't think MWI would be uncountable in most circumstances. Because it's only a Low 2-C space being multiplied infinitely, which is just 2A. Even if the branches infinitely branch that's still just 2A because the original space is a finite number.

 

[Firestorm808]

Even if the branches infinitely branch that's still just 2A because the original space is a finite number.

I see. So, when working with a narrative "branch" mechanic, you need a description of the original space or "trunk" itself having an infinite number of separate temporal layers making it up.

We have the following parameters:

1. We have an infinitely long timeline (A)
2. (A) is made up of an infinite number of separate temporal layers
3. (A) has an infinite number of branch points

 

[Qawsedf234]

So, when working with a narrative "branch" mechanic, you need a description of the original space or "trunk" itself having an infinite number of separate temporal layers making it up.

The point is that in set theory there's different infinite groups that you can compare stuff to

A set of infinite natural numbers can fit into a set of integers that fit into a set of any rational number which fits into a set of real numbers.

For it to be Aleph-1 you have to have a set of all infinite sets. It's why just having a bigger multiverse or whatever isn't enough, as there's larger infinite sets that can contain lower ones.

The point of a recursive set is that there's so many larger infinites that it would necessitate an Aleph-1 set to contain them all, since it would be a set of all Real Numbers.

 

[Firestorm808]

I understand the mathematical perspective.

This thread aims to determine the common ways it can be portrayed in a traditional narrative. Since it's based on set theory, using a typical 3-D object instead of something more conceptual or metaphysical as a basis isn't as practical. It's easier for me to use timelines since they are metaphysical objects.

For the sake of the example, I'll be using "Natural, Whole, etc" to separate the sets.

A Single Number = A Single Separate Spactio-Temporal Layer
Natural = Aleph-0 = An infinite number set of Spactio-Separate Temporal Layers which fit inside a Single Timeline
Integer = Aleph-1 = An infinite number set of Timelines in which an infinite number set of Separate Temporal Layers fits inside each
Rational = Aleph-2 = The Infinite-Sized Number Set Realm, in which an infinite number set of Timelines fits inside

 

[Qawsedf234]

For the sake of the example, I'll be using "Natural, Whole, etc" to separate the sets.

A Single Number = A Single Separate Spactio-Temporal Layer
Natural = Aleph-0 = An infinite number set of Spactio-Separate Temporal Layers which fit inside a Single Timeline
Integer = Aleph-1 = An infinite number set of Timelines in which an infinite number set of Separate Temporal Layers fits inside each
Rational = Aleph-2 = The Infinite-Sized Number Set Realm, in which an infinite number set of Timelines fits inside

You're close there, but to quote the FAQ

Thus, only an uncountably infinite number of universes actually makes any difference in terms of Attack Potency, at this scale.

To use mathmatics, only "Real" or "Irrational" sets are an uncountable infinite

Recall that two sets are equivalent if they can be placed in one-to-one correspondence (so that each element of the first set corresponds to exactly one of the second). For finite sets this means they have the same number of elements.

An infinite set is a set which is equivalent to a proper subset of itself. For example, the set of integers is equivalent to the set of even integers--a proper subset (to see this, just note f(n)=2n is a one-to-one function from the integers to the even integers).

This definition has some amusing consequences. For example, suppose we had a hotel with an infinite number of rooms numbered 1, 2, 3, 4, ..., and no vacancy (every room is filled). We still have room for another person! All we need to do is to have each person move over one room (1 goes to 2, 2 to 3, ..., n to n+1...). In fact, even if it is full, it has room for as many folks as are already in it (just send 1 to 2, 2 to 4, 3 to 6, ... , n to 2n, ..., this leaves 1, 3, 5, ... empty). The moral is that "the number of" elements in an infinite set (its cardinality) does not behave like it does for a finite set.

Infinite sets are divided into two types: those which are equivalent to a subset of the integers (called countable) and those which are not (called uncountable). The primes, composites, and positive integers are clearly countable. But so are the rational numbers, the set of polynomials with integer coefficients, and hence the algebraic numbers. Uncountable sets include the real and complex numbers, the irrational numbers, the transcendental numbers, and the power set of any countably infinite set.

So in this case, you'd only get Aleph-1 / An Uncountable Infinity at the Real Number Stage or if you can prove that universes work on irrational number logic (which I don't believe can be done). So for your example, Natural, Integer and Rational numbers would still be 2A or just higher into 2A. Only with Real Numbers would you get Low 1-C.

For the multiverse example, I guess I didn't use the correct language. It would be more like a power set than a Real Number set, though both would result in the same thing.

 

[Firestorm808]

Ah, okay. So only the below would be the correct Alephs?

A Single Number = A Single Separate Spactio-Temporal Layer
Aleph-0 = An infinite number set of Spactio-Separate Temporal Layers which fit inside a Single Timeline
Aleph-1 = An infinite number set of Timelines in which an infinite number set of Separate Temporal Layers fits inside each

 

[Firestorm808]

"Being “infinitely” stronger than this level, unless uncountably so, does not qualify for any higher tier."

An example of being "infinitely” stronger could be described by some in-narrative power measurement scale. It could be some sort of stats game narrative, like Solo Leveling or Shield Hero.

Let's say a Hunter's Strength is proportional to their STR stat. Let's say a hunter is Level 1 with 5 STR. Then we have a Hunter with Level X with Infinite STR.

Then you move from the Hunter STR set to the God STR set.

Infinite Hunter STR = 1 God STR

An Infinite Hunter STR wouldn't be uncountable higher. You could say they are infinite 3-D strength tiers.

An Infinite God STR would be uncountably stronger than the 5 Hunter STR set. This would put it in the 4-D strength tier

 

[Qawsedf234]

An Infinite Hunter STR wouldn't be uncountable higher. You could say they are infinite 3-D strength tiers.

From what I understand of it, they would be a bigger infinity without being an Uncountable infinity.

 

[Firestorm808]

From what I understand of it, they would be a bigger infinity without being an Uncountable infinity.

To clarify in the game-like narrative example,

Where an Infinite Hunter STR = 1 God STR

An Infinite or 5 God STR would be uncountably stronger than a 5 Hunter STR?