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So there's been a lot of discussion regarding the standards for higher additional/higher dimensions. Through these two statements from DDT and Ultima, it was established that overarching timelines aren't automatically Low 1-C because spatiotemporal separation doesn't inherently introduce new axes/dimensions of time, and a single time dimension can service a construction of a timeline encompassing a multiverse. With all the debate over technicalities of when overarching timelines could qualify for Low 1-C, I have to summarize my concerns into a simple yes/no question.Are overarching timelines Low 1-C when there is confirmation for the lesser timelines it encompasses harboring their own time dimensions/axes?
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 comparision that allows scaling to be made.
Q: How do temporal dimensions impact on tiering?
A: The relationship between the spatial dimensions of a universe and the additional temporal dimension(s) may be visualized as something akin to the frames of a movie placed side-by-side. Basically, the time-like direction may be thought of as a line comprised of uncountably infinite points, each of which is a static "snapshot" of the whole universe at any given moment, with the set of all such events comprising the totality of spacetime.
This structure can then be generalized to any amounts of dimensions, and is also the reason destroying a spacetime continuum is a greater feat than destroying only the contents of the physical universe (Low 2-C, rather than 3-A or High 3-A). So, for example, a spacetime continuum comprising two temporal dimensions (Instead of just one) would have an additional time direction whose "snapshots" correspond to the whole of a 4-dimensional spacetime, and so on and so forth.
The main purpose of this forum is to discuss how to properly index the statistics of characters from a wide variety of different fictional franchises.