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Tiering System Revisions - Part 3

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Antvasima said:
So to summarise the alternatives here, if I have understood them correctly, should we go with this:
1-A: Finite outerversal hierarchy

1-A+: Infinite outerversal hierarchy

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)

Or this:

1-A: Finite outerversal hierarchy

High 1-A: Infinite outerversal hierarchy

0: Immeasurably transcends any infinite outerversal hierarchies

Or this:

1-A: Finite and infinite outerversal hierarchies

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)

Please feel free to make corrections, if I have misunderstood something.
Click to expand...
"Boundless" and "transcends any infinite hierarchies" sounds similar (otherwise, let us star "Featherine vs Azathoth" and "Yog Sothoth vs The Creator" discussions at the same time, but both of them cannot be proper debated). Option 2 is the most "solid" ground.

I think so.

EDIT:

1-B = finite dimensional.

High 1-B = infinite dimensional

1-A = finite outerversal

High 1-A = infinite outerversal

It seems nice and more or less "logical".
 
Where would classic Marvel stand with it's uncountable and transfinite number of layered dimensions? Would it have a "High 1-B+" rating? Because this would give Classic Marvel characters an advantage over conventional Infinite dimensional characters
 
I've been allowed to post this despite not being a staff member-

What is wrong with the current tier list ?

All of this seems to be unnecessarily complicated. 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 ? Not to mention it isn't really related to bigness but rather to sets not having bjection/1to1 correspondence. These are complex mathematical ideas that have no connection to a tierlist of dimensional tiers. We're not comparing sets of integers here ! 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. You can name the same infinite number of dimensions after the set of all rational numbers (uncountable) or after the set of all rational numbers (countable), it's the same either away.

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.

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 such as- https://medium.com/@VitalikButerin/cantor-was-wrong-debunking-the-infinite-set-hierarchy-e9ba5015102, https://www.academia.edu/37229455/CONTRA_CANTOR_HOW_TO_COUNT_THE_UNCOUNTABLY_INFINITE_, http://www.thomaswhichello.com/?page_id=372 and https://medium.com/@freefrancisco/was-cantor-wrong-a30802cf3152 . Why do we want it on our tier list ?

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.

The tierlist is fine as it is, there's no need to go ultra-scientific, if we really followed real life physics to a T, most of the characters on our tierlist would be in a different tier and AP wouldn't scale to strength but to speed (F=MxA), etc.
 
the thing is this isnt relevant when it comes to tier 1s which is using the amount of dimensions in a tiering, the only thing that has been changed is the quantity/quality of tier 1-As and being more accurate when it comes to how far 1-A could be from the old system. umineko, masada, CM characters are only said to be on 1-A which is beyond dimensions in the old tiering. but this new tiering specifies what positions they're going to be. this is nothing about scientific when it comes to 1-As when all of this will include set theory and cantor philosophy to translate it to fiction which was said above. Also no mathematicians never disagreed to it but they wanted to expand to his idea hence theres thing that we can axiomatically erase and using continuum hypothesis method.
 
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.
 
You're confusing "uncountable infinity" with "absolute infinity". Mathematicians don't accept Absolute Infinity.
 
It's less about just throwing votes and more about essentially just figuring out how we'll handle the Outerversal Tiers. Everything else is pretty much already set in stone. And nobody is particularly against the changes. It's just the minutia of 1-A / High 1-A and 0 that is being discussed. Everything else isn't of anyone's major concern.
 
Antvasima said:
So to summarise the alternatives here, if I have understood them correctly, should we go with this:

1-A: Finite outerversal hierarchy

1-A+: Infinite outerversal hierarchy

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)

Or this:

1-A: Finite outerversal hierarchy

High 1-A: Infinite outerversal hierarchy

0: Immeasurably transcends any infinite outerversal hierarchies

Or this:

1-A: Finite and infinite outerversal hierarchies

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)

Please feel free to make corrections, if I have misunderstood something.
Click to expand...
Returning to the current key issue here.
 
Now that I think about it... R^R should be definitely Low 1-A, it's beyond-dimensional size anyway and fits with the beyond-dimensional existence page. Even R^Infinity cannot access R^R by stacking infinites.
 
@Sera

Please explain. I am unfamiliar with the term.
 
R = Real number (all real numbers). R^3 = the math behind three-dimensional, R^4 = the math behind four-dimensional, etc. R^Inf = the math behind infinite-dimensional.

R^R is basically uncountable infinite dimensions, which is like "pseudo-outerversal" and is definitely beyond-dimensional. It should be Type 1 BDE instead of "non-dimensional".

As Ultima said the system even now is based on size, so all "oversized" quantities "those greater than infinite-dimensions" should be in the 1-A category.
 
Okay. I suppose that I will have to try to be flexible and accept that then.
 
If Ultima, Sera and Kingpin all consider uncountably infinite dimension to be appropriate for low 1-A, then I guess it should probably be fine

I'm in support of that option, I'm also glad it keeps finite hyperversal in the tier I think it should be
 
Antvasima said:
So to summarise the alternatives here, if I have understood them correctly, should we go with this:

1-A: Finite outerversal hierarchy

1-A+: Infinite outerversal hierarchy

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)

Or this:

1-A: Finite outerversal hierarchy

High 1-A: Infinite outerversal hierarchy

0: Immeasurably transcends any infinite outerversal hierarchies

Or this:

1-A: Finite and infinite outerversal hierarchies

High 1-A: Immeasurably transcends any infinite outerversal hierarchies

0: Boundless (Transcends High 1-A by the same degree it transcends Low 1-A)
Click to expand...
So, about this part then...
 
I am fine with either 1 or 3. It doesn't particularly concern me whether infinite hierarchies get a + treatment or not, I just don't think an entirely different tier for them is necessary

Although given Sera's comment, are we still sure about not having low 1-A?
 
I suppose so, if the other staff members think that it is a good idea.
 
Real quick, I know this is more-or-less a staff-only thread with some exceptions, so this will probably be my only comment here. Regarding all that has been discussed on the subject of real numbers, inaccessible cardinals and everything else that's been discussed in these revision threads, is it going to be going to be intergrated into the tier system page or would it be better relegated to its own page? Because I would personally be interested in a page specifically dedicated to explaining the concepts discussed in these threads, if only for clarification, at least.
 
Ultima Reality said:
So, what now? Are we going to go by what I suggested here or...?
Click to expand...
To implement your suggestion in that post, we need to make a thread for redefining the tiers of all high tier verses.
 
Sera EX said:
R = Real number (all real numbers). R^3 = the math behind three-dimensional, R^4 = the math behind four-dimensional, etc. R^Inf = the math behind infinite-dimensional.
R^R is basically uncountable infinite dimensions, which is like "pseudo-outerversal" and is definitely beyond-dimensional. It should be Type 1 BDE instead of "non-dimensional".

As Ultima said the system even now is based on size, so all "oversized" quantities "those greater than infinite-dimensions" should be in the 1-A category.
Click to expand...
Just thought I should mention something. X^Y is typically defined as the set of all functions from X to Y. R^n is typically identified with n-dimensional space, i.e. all n-tuples (x,y,z...). Under this conception, R^R would really be R^c, where c=|R| is the cardinality of the continuum. This means R^R is continuum dimensional. c is uncountable, but it is possible that there are infinites k smaller then c, so it is misleading to say R^R is uncountably infinte dimensions. There are many different flavors of uncountable infinity. I apologize that this is a staff only thread, but I just thought it might be important to mention that there are different degrees of uncountable infinity, and even different types if you work in certain set theories. For example, c=|R| might not even exist, in which case the notion of "uncountable" starts to diverge from intuition.

Reference: Thomas Jech's Set Theory. The non-existence of c is mentioned in part 6 of Kanamori's The Higher Infinite.
 
@MasterOfArda I'm not learned enough to really comment on your points, so my one comment is, is your issue solved if we assume that the Continuum Hypothesis holds, or is your point independent of that?
 
Yes, it is resolved. CH is equivalent over ZFC to the statement there is no uncountable cardinal k<c, i.e. that c is the smallest uncountable infinity. But, there are still many different uncountable infinities even assuming CH. For exmaple, ╬ÿ=c+, the smallest infinity greater then c (Assume AC), and then ╬ÿ+=c++, and so on.
 
Yes but since our system will assume CH holds, the tier would be fine. It's baseline uncountably infinite dimensions and above. Anything above R^R would be in that tier or a higher tier.
 
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