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Here infinitely sized means infinite number(cardinality) as the whole heading of the FAQ even implies it.
You're mistaken, it is not solely talking about quantity and cardinality. It is talking about size (which is related, but not solely dependent on, those two things), and mentions that an uncountable number of universes is one of two ways to bridge the gap to Low 1-C, in absence of an explicit statement about its dimensionality. It is helpful because it clarifies that a multiverse being infinitely sized is not Low 1-C.The whole thing is talking about quantity and cardinality when referring to size and whether some higher quantity of universes will imply a higher dimesnionality and it clarified that yes it would only when the quantity is uncountably infinite or higher. So, no to any reference for spatial size in that FAQ?
This is made even clearer in the section titled "Is a structure bigger than a 2-A structure Low 1-C by default?"Q: Is destroying multiple infinite multiverses a better feat than destroying a single one?
A: 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.
Q: Is a structure bigger than a 2-A structure Low 1-C by default?
A: No, the default assumption is that this is not the case. "Bigger" could mean having more 2-A structures and, as explained in greater detail previously, having more 2-A structures, or even infinitely many 2-A structures, unless uncountably infinite many, won't scale above a single 2-A structure in size. This is due to these structures actually have the same size as a baseline 2-A structure.
However, if "bigger" is indicated to mean a size difference that makes the structure qualitatively superior to a 2-A structure the structure qualifies for Low 1-C unless the fiction specifies otherwise.
So, again, the FAQ is also referring to size, not specifically cardinality. The section on cardinality comes afterwards, and a careful reading of it reveals that your interpretation of the earlier entries is not valid:To elaborate, a structure larger than 2-A meets the requirements for qualitative superiority over them if it either explicitly mentions an uncountably infinite number of universes or has portrayals/statements of being bigger in size than 2-A structures to the point that even infinite multipliers on top of the size of that structure are of no relevance to it. Multiversal structures past Low 2-C frequently have a distance of unknown length along a 5th dimensional axis separating them. That isn't automatically Low 1-C, as for Low 1-C the distance must be known to be of non-insignificant size.
To recap this. Cardinality is not inherently related to scaling. The "cardinality" of everything from Tier 11 to 2-A is the same Aleph-0. One way in which cardinality can be relevant to scaling is when an Aleph-1 number of universes is involved, which indicates Low 1-C.Q: How do cardinal numbers relate to tiering?
A: Firstly, it should be highlighted that asking about the tier of a cardinal number is effectively a meaningless question when the quantity which it is denoting is not specified in the question as well, and makes as much sense as asking "What tier is the number 8?"
Let's take the smallest infinite cardinal (aleph-0, or ℵ0, the cardinality of countably infinite sets) as an example in this case: A set comprised of a countably infinite number of 0-dimensional points is itself a 0-dimensional space under the usual notions of dimensionality, being thus still infinitely small. Meanwhile, a countably infinite number of planets is High 3-A, a countably infinite number of universes 2-A, and countably infinite dimensions High 1-B.
We then move on to the power set of ℵ0, P(ℵ0), which is an uncountably infinite quantity and represents the set of all the ways in which you can arrange the elements of a set whose cardinality is the former, and is also equal to the size of the set of all real numbers. In terms of points, one can say that everything from 1-dimensional space to (countably) infinite-dimensional space falls under it, as all of these spaces have the same number of elements (coordinates, in this case), in spite of each being infinitely larger than the preceding one by the intuitive notions of size that we regularly utilize (Area, Volume, etc.).
On the other hand, an P(ℵ0) number of universes is Low 1-C, and a similar number of spatial dimensions/layers of reality is Low 1-A.
However, the same does not necessarily apply when approaching sets of higher cardinalities than this (Such as P(P(ℵ0)), the power set of the power set of aleph-0), as they would be strictly bigger than all of the spaces mentioned above, by all rigorous notions of size, regardless of what their elements are. From this point and onwards, all such sets are Low 1-A at minimum.
Do note, however, that these infinities must specifically refer to elements that physically exist within a verse's cosmology. Them existing as in-universe mathematical concepts is not sufficient for anything to scale to them, unless there is a direct comparison that allows scaling to be made.
In the earlier FAQ entries, it is clarified that being bigger than a 2-A structure is not enough, unless specifically the 4-D space is regarded as infinitesimal to the structure or the number of universes within it has a higher cardinality. Conventional notions of "size" without those two clarifications (such as being called infinitely sized, as specified by the multiple references to an "infinitely sized multiverse" cannot bridge the gap between 2-A and Low 1-C. The multiverse being called "infinite" or "infinitely sized," such as in the Demon World's case, does not provide further evidence for its tier beyond the bare fact of it containing these Low 2-C structure, which is definitively 2-A.
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