Some questions regarding the Tiering System

[Shadowbeast]

Here I have two doubts about the Tier System of the wiki, if someone could answer me and justify/refutate them, i would appreciate it.

Tiering System

The following is a comprehensive overview of the hierarchical system the VS Battles Wiki utilizes to properly categorize and index fictional characters, entities, and objects based on the scale of their feats and the varying scopes that they can affect or create/destroy. Though Destructive...

vsbattles.fandom.com

1-First, the current wiki says that the standard/baseline Outerserval level can be mathematically defined as ℵ2 and onwards, just for being superior to Low-Outerversal, which is defined as ℵ1. But wouldn't this contradict the same scale? because ℵ2 and onwards is tied to the set theory, which is a mathematical concept.

Set theory - Wikipedia

en.m.wikipedia.org

And according to the wiki, Outerversal is something abstract and transcendent in relation to any dimensional constant, transcending the concepts of space and time itself. Therefore, shouldn't ℵ2 and onwards be Low 1-A aka Low Outerverse instead of Outerversal? this by taking into account the same system level that the wiki establishes.

Tiering System FAQ

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. In a way, yes, though not how most would...

vsbattles.fandom.com

2-In the Tiering System FAQ, it also says that a finite set of Multiverses Aka a finite Megaverse, is equal to a single Multiverse just because they are countably infinite and not uncountably infinite, here is the thing i'm refering to:

"In spite of what our intuitions may tell us, destroying or fully affecting multiple infinite-sized multiverses is in fact not better than doing the same to a single infinite multiverse, and thus, not above the "baseline" for 2-A.
The reason is that the total amount of universes contained in a collection of multiple infinitely-sized multiverses (even one consisting of infinitely many of them) is in fact equal to the amount of universes contained in a single one of the multiverses that form this ensemble: It is countably infinite, as the union of countably-many countable sets is itself countable, and thus does not differ in size from its components. The only general difference between multiple infinitely-sized multiverses and a single one is representation. What is considered to be multiple multiverses in one fiction could be considered a single multiverse in another, and vice versa, without the objective properties of those collections of universes changing. The only difference is where an author decided to draw the line between what belongs to the same multiverse and not. Thus, only an uncountably infinite number of universes actually makes any difference in terms of Attack Potency, at this scale. This illustrates some of the more unintuitive properties of sets with infinite elements: Namely, given a set X, it being a subset of another set Y does not imply that Y > X in terms of size. An example of this is how the set of all natural numbers contains both the odd numbers and even numbers, yet all of these sets in fact have the same number of elements."

However, wouldn't this be false? because there's no proof that just because it is an infinite countable set, it would have to be necessarily equal. If someone has an additional infinity in his first infinite set, this will objectively make him superior, a weapon that has two bullets is not the same as the one that only has one bullet.

 

[Guardian_Doge]

Outerversal is something abstract and transcendent in relation to any dimensional constant, transcending the concepts of space and time itself.

Outerversal is defined as being above the Geometric dimensions that can be made through real coordinate space or R^n, hence biject to ℵ1 [in the Continuum Hypothesis] due to real numbers (or complex numbers) making higher planes. It doesn't explicitly have to be conceptual transcendence to space and time, I think your mistaking some of this system for CSaP.

Hence why I am confused to this:

Therefore, shouldn't ℵ2 and onwards be Low 1-A aka Low Outerverse instead of Outerversal?

What exactly is the question being asked here, could you elaborate on it please.

However, wouldn't this be false? because there's no proof that just because it is an infinite countable set, it would have to be necessarily equal. If someone has an additional infinity in his first infinite set, this will objectively make him superior, a weapon that has two bullets is not the same as the one that only has one bullet.

In Set theory, there's a concept noted as transfinite recursion and induction, let's briefly go over the former:
“If A is a well ordering, suppose you have function G, from the set and initial segments of the function of B to B, you build a function f from A to B. Which satisfies (*) that every t belongs to A , function t is equal to procedure G where F is restricted to previous values (segment t)”

What this means is, in recursion, it takes the previous functions to build the next higher one. So if we simply have a couple of infinite multiverses let's say three, there's ironically, no proof that states these three multiverses are > in size to just one multiverse. Because in this case it's just addition..of the same infinity, not a "powerset" as they call it, hence would not make a higher value of it.

 

[Shadowbeast]

What exactly is the question being asked here, could you elaborate on it please.

The question was about the mathematical representation of the Outerversal Tiers, because ℵ2 and onwards is tied to the Set Theory, which I thought by the Outerversal concepts of the same wiki, should be the mathematical representation of Low Outerversal(Low 1-A) which according to the wiki, is represented mathematically only by ℵ1(and when I looked deeper, I thought it should be represented by ℵ2 and onwards too, when i thinked that the mathematical representation of baseline Outerversal{1-A} was wrong.)
But i wasn't sure about this, hence why i asked here, to see if i wasn't wrong about somenthing.

 

[Cat275]

Here I have two doubts about the Tier System of the wiki, if someone could answer me and justify/refutate them, i would appreciate it.

Tiering System

The following is a comprehensive overview of the hierarchical system the VS Battles Wiki utilizes to properly categorize and index fictional characters, entities, and objects based on the scale of their feats and the varying scopes that they can affect or create/destroy. Though Destructive...

vsbattles.fandom.com

1-First, the current wiki says that the standard/baseline Outerserval level can be mathematically defined as ℵ2 and onwards, just for being superior to Low-Outerversal, which is defined as ℵ1. But wouldn't this contradict the same scale? because ℵ2 and onwards is tied to the set theory, which is a mathematical concept.

Set theory - Wikipedia

en.m.wikipedia.org

And according to the wiki, Outerversal is something abstract and transcendent in relation to any dimensional constant, transcending the concepts of space and time itself. Therefore, shouldn't ℵ2 and onwards be Low 1-A aka Low Outerverse instead of Outerversal? this by taking into account the same system level that the wiki establishes.

Aleph 2 dimensionallity is bigger than Real coordinate spaces.

They are strictly greater than Aleph 1
(Uncountably infinitely greater like i guess.)
so if you have a layer of existence that scale to Aleph 2 normally you would also be strictly greater than real cordinate space since real coordinate spaces stops at
Low-1a(Aleph 1) at best for having a space correspondance of all real numbers.
(Since they have their own real number line.)

 

[Cat275]

However, wouldn't this be false? because there's no proof that just because it is an infinite countable set, it would have to be necessarily equal. If someone has an additional infinity in his first infinite set, this will objectively make him superior, a weapon that has two bullets is not the same as the one that only has one bullet.

Infinite additions won't really be stronger than one infinite.

You need to have a power set or a collection of subset to make a stronger or bigger infinity rather than adding infinities up.
(It's like 1 × 1)

And there are summaries that would make equations such as this different.
(If you want to use it of course.)

 

[Cat275]

The question was about the mathematical representation of the Outerversal Tiers, because ℵ2 and onwards is tied to the Set Theory, which I thought by the Outerversal concepts of the same wiki, should be the mathematical representation of Low Outerversal(Low 1-A) which according to the wiki, is represented mathematically only by ℵ1(and when I looked deeper, I thought it should be represented by ℵ2 and onwards too, when i thinked that the mathematical representation of baseline Outerversal{1-A} was wrong.)
But i wasn't sure about this, hence why i asked here, to see if i wasn't wrong about somenthing.

No (ℵ2,,,,,,,,ℵ99 and so on) is bigger than real coordinate spaces they should be beyond dimensions in a way if they have layered existence with this mathematics or something like that.