All of this seems to be unnecessarily complicated
I am aware that it is complicated to most people, hence why I said multiple times in the thread that all of this stuff is going to be explained neatly and concisely in separate explanation pages. They aren't going to be in the main Tiering System page, and will mostly be just clockwork that remains under the hood of the whole thing.
Countable and uncountable infinities ? Really ? That is something that mathematicians are still heavily debating and disagreeing on and we are putting it on our tier list ?
I have no idea what you are talking about. The concept of infinite sets with differing cardinalities is something accepted and objectively proven, and that is used in many areas of Mathematics (such as Topology, for example), not something that is still being contested or anything of the sort. The people who disagree with it are mostly those who adopt Finitism and don't even believe infinite sets are a thing in the first place, so they just exclude the axiom of infinity from their book.
Not to mention it isn't really related to bigness but rather to sets not having bijection/1to1 correspondence
It is, though? If a Set A has no bijection unto a Set B, then those two collections have different cardinalities, and thus different sizes. This is a pretty basic notion.
You can't even differentiate between a uncountably infinite number of dimensions and a countable infinite number of dinensions, dinensions have no numbers attached to them.
The "dimension" of a given mathematical space is just the cardinality of its
basis (i.e the number of linearly independent vectors defined in it), you can just equate it to any given Cardinal Number. The measure through which we generalize this notion and assign sizes to subsets of such a space may turn uninsteresting or straight up useless after a certain point, but that doesn't really mean you can't have a space whose dimension has cardinality greater than a countable set.
These are concepts designed for integers not for counting objects. They don't hold true for the physical universe. If you take all of the people out of Cantor's hotel you can fit them all into Hilbert's. An infinity is just an infinity.
That's sort of irrelevant, since you can make a set out of nearly anything anyways. Them not applying to the physical universe isn't exactly relevant either, since we are dealing with fictional settings here, and we can just equalize sizes anyways, there's nothing wrong with saying a given space has size
equivalent to a given infinite cardinal number, it's pretty much something we already do, just more formalized.
I also don't know what Hilbert's Hotel has to do with this, considering Hilbert himself was heavily supportive of Set Theory and all that jazz.
And many modern mathematicians disagree on this whole uncountable infinity phenomenon even existing. Many mathematicians believe that there is no such thing as an uncountable infinity. Why do we want it on our tier list ?
See above; The notion of infinite sets of differing sizes is already accepted in mainstream mathematics, and no one ever truly disproved it, as far as I've seen.
I should also note the first link you posted is an april fools joke.
As for all the sub-tiers of 1A, they just strike me as unnecessary, we'll never find any characters to fill half of them.
There are actually quite a few characters that can potentially qualify for them, I can name them if you want.
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