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Low 1-A Wiki Wide Tiering Revision, Beyond Dimensions.

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DontTalkDT said:
Oh yeah, you have a point. I wasn't quite careful with the exact formulation there. In fact, I was double not careful regarding something else as well, so I have to revise some stuff I said earlier, as I came up with a good argument for why it's wrong.

The case that I literally wrote there equates to "can destroy an n-dimensional space for every natural number n." In this you're correct. That would be arbitrarily high into 1-B, just below High 1-B, and we would not give it a +1 ('cause this statement implies to qualitative superiority over the spaces). But if we added transcendence then it would be High 1-B.

If it's instead "can destroy all the nested n-dimensional spaces at once" then it's something infinite dimensional, because the unification of all finite-dimensional spaces is infinite-dimensional. Here lies the second part I was not careful with. Let's say we, somewhat intuitively, identify the union of all finite-dimensional spaces with the space of infinite sequences R^N. (I say intuitively, as one could consider the 1D space as the subspace build by infinite sequences in which only the first entry may change, the 2D space the one where the first two may change etc. and with no specific limit regarding distance. i.e. only equipped with the product topology) Now, despite what it might look like at first, the cardinality of the dimension of R^N is not aleph_0, but aleph_1. (Here's a proper explanation on that.) But I kinda didn't think that far when I made my initial statement.

Hence, in the case of destroying all finite-dimensional spaces at once, the tier would be Low 1-A. Honestly, that's a much better reason to start the (Low) 1-A realm there instead of at aleph_0, than that separation argument or whatever it was...

With that in mind I then have to correct earlier statements I made as well. For this, and none of the other reasons that were given before, I agree that it makes sense to tier transcendence over arbitrarily many (finite) dimensions as 1-A (aleph_2), as being 1 infinity above the unification of finite-dimensional spaces is aleph_2, as the unification itself is aleph_1.

So, while for different reasons, I suppose I'm actually fine with your initial 1-A proposal.
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Why did transcending Infinite Dimensions in the tier page only equal to Aleph-1 then?

So what will the tier of these statements be?
 
Rakih_Elyan said:
Why did transcending Infinite Dimensions in the tier page only equal to Aleph-1 then?
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Because, as strange as it is, transcending infinite dimensions can mean to transcend a space with aleph_0 dimensions, which would then be aleph_1. Spaces of that nature exist, like for instance the space of finite sequences. (Although they all are not Hilbert spaces)
It's somewhat a weird mathematical quirk that if you cross from finite to infinite via product spaces, you jump over one level of infinite dimensional spaces. But that's just how it is.

(Edit: Btw. if anyone feels like having a talk over whether it might be more intuitive to interpret the "union" of all finite-dimensional spaces as space of finite sequences instead of space of infinite sequences let me know. I'm all up for that, as I'm actually split on which is more intuitive. There are different POVs to be had here, depending on whether one adds an axis via a cartesian product infinite times (which results in the space of infinite sequences) or takes the literal union of all points in the sequences space representation (that results in finite sequences))

Edit 2: I guess ultimately it comes down to whether one wishes to assume completeness. Using the finite sequences means that if you set one coordinate in each of the dimensional axis of the finite dimensional spaces you can get a point that is not in your total space, which is somewhat unintuitive. It basically means taking a certain combination of positions along each axis at once is impossible. On the other hand, was such a point not part of any of the finite-dimensional spaces, so perhaps we don't care for it after all.
Rakih_Elyan said:
So what will the tier of these statements be?
Click to expand...
Well, 1., 2. and 4. stay as I explained earlier. And 3. would be upper-end 1-B, like Agnaa said.
 
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Rakih_Elyan said:
To 1-A or Low 1-A?

So a character that transcend infinite sequence of dimensions is 1-A?
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1. was however many dimensions the verse is known to have +1.
2. was however many dimensions the verse is known to have.
4. was however many planes of existence the verse is known to have.

3. Is... well, 1-B if we take it as "no matter how many dimensions there are they can destroy them".

If it's "They can destroy all finite dimensions at once" we have to think about that whole sequence space business, i.e. whether the space of finite sequences or space of infinite sequences is better. If finite sequences is better (incomplete space, but in exchange only the union) then it's High 1-B. If infinite sequence space is better (complete space and natural continuation of the product space idea, but some points contained that are not in any finite-dimensional space) then it's Low 1-A.
And if we ask for the ranking of "Transcends all finite dimensional spaces" we would be either Low 1-A or 1-A depending on which option we take.

Honestly, I'm kinda jumping back and forth between which option I prefer right now. Low 1-A might make more sense after all... Then again, this might again be drifting off from what the thread was about? In that case it will become a topic for a next thread... honestly, might be best to handle it separately.
 
DontTalkDT said:
That's for Agnaa to say.
Click to expand...
I don't understand it enough to take issue with it or vehemently assert it. If we practically agree but for different reasons, then that's fine.

And to repeat something I mentioned before, we seem to disagree a bit on how many cases to apply this to, with me accepting more than DT but fewer than Ultima, but I don't evaluate high-tier verses anyway, and out of the two I'd rather defer to DT.
 
KLOL506 said:
So, what are the conclusions reached?
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DontTalkDT said:
1. was however many dimensions the verse is known to have +1.
2. was however many dimensions the verse is known to have.
4. was however many planes of existence the verse is known to have.

3. Is... well, 1-B if we take it as "no matter how many dimensions there are they can destroy them".

If it's "They can destroy all finite dimensions at once" we have to think about that whole sequence space business, i.e. whether the space of finite sequences or space of infinite sequences is better. If finite sequences is better (incomplete space, but in exchange only the union) then it's High 1-B. If infinite sequence space is better (complete space and natural continuation of the product space idea, but some points contained that are not in any finite-dimensional space) then it's Low 1-A.
And if we ask for the ranking of "Transcends all finite dimensional spaces" we would be either Low 1-A or 1-A depending on which option we take.

Honestly, I'm kinda jumping back and forth between which option I prefer right now. Low 1-A might make more sense after all... Then again, this might again be drifting off from what the thread was about? In that case it will become a topic for a next thread... honestly, might be best to handle it separately.
Click to expand...
 
So what, if anything, should be changed in our tiering system if DontTalk's quoted conclusions in the last preceding post above are accepted?
 
I don't think anything on the Tiering System page itself needs to be changed. This is mostly a thing of interpretation.

Maybe something should be changed in the Tiering System FAQ? In particular, the 8th, 10th, 12th, and 13th questions/answers should be looked at. But from a quick glance, most of them seem consistent with what DontTalk's suggesting.

In terms of practical changes, this would mostly involve taking another look at verses rated 1-A or higher, to see if they meet these stricter standards.
 
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Delete those post please, this is staff discussion thread.

I admit that I bumped this thread too early, but your post above bring nothing to the matter of the thread.
 
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Can we change the FAQ accordingly to what DT proposed and create a further CRT to address the affected verse?
 
Agnaa said:
We can't since no-one's suggested any. But if you or someone else does, we could have a look at them.
Click to expand...
BTW, what do you think of DT's new comment?

DontTalkDT said:
1. was however many dimensions the verse is known to have +1.
2. was however many dimensions the verse is known to have.
4. was however many planes of existence the verse is known to have.

3. Is... well, 1-B if we take it as "no matter how many dimensions there are they can destroy them".

If it's "They can destroy all finite dimensions at once" we have to think about that whole sequence space business, i.e. whether the space of finite sequences or space of infinite sequences is better. If finite sequences is better (incomplete space, but in exchange only the union) then it's High 1-B. If infinite sequence space is better (complete space and natural continuation of the product space idea, but some points contained that are not in any finite-dimensional space) then it's Low 1-A.
And if we ask for the ranking of "Transcends all finite dimensional spaces" we would be either Low 1-A or 1-A depending on which option we take.

Honestly, I'm kinda jumping back and forth between which option I prefer right now. Low 1-A might make more sense after all... Then again, this might again be drifting off from what the thread was about? In that case it will become a topic for a next thread... honestly, might be best to handle it separately.
Click to expand...
 
Luckyfun said:
So transcending infinite dimensions now only reach low-1A?

What about transcending the concept of dimensions?
Click to expand...
1 transcendence higher than the number of dimensions the verse is known to have.
 
Luckyfun said:
What about transcending the concept of dimensions?
Click to expand...
We already address that claim

Q: What tier is transcending dimensions?​

A: As specified above, a "dimension" is nothing more than a set of values representing a given direction within a system, and a multi-dimensional space can itself be thought of as a multiplication of several "copies" of these sets. For instance, the 3-dimensional space in which we live is often visualized as the set of all 3-tuples of real numbers (Thus, taking its values from the real number line, R), and is thus the result of the iterated multiplication: R x R x R = R³, likewise, 4-dimensional space is the set of all 4-tuples of real numbers, and is thus equal to R x R x R x R = R⁴, and so on and so forth.

Practically speaking, this means that there is no limit for the number of dimensions which a space can have whatsoever, and one can construct spaces whose dimension corresponds to any cardinal number, including the infinite ones mentioned above. It is not even necessary for us to restrict ourselves to values taken from the real numbers, either: It is also possible to define the space of all n-tuples of cardinal numbers (Which takes its values from V, the class of all sets)

As a result, it is not at all feasible to take any statements involving a character existing "beyond dimensions" at face value, as this would lead to extremely inflated ratings largely dependent on No-Limits Fallacies. Therefore, such descriptors are to be evaluated while taking into account the number of dimensions which the verse has been shown to entertain; for example, a character stated to exist above physical dimensions in relation to a 4-dimensional cosmology would be Low 1-C with no further context.
Click to expand...
 
Rakih_Elyan said:
Change the FAQ by erasing the notion of accessing 1-A without mention of infinity, since we require it now.
Click to expand...
I don't think that's sufficient, since DT is okay with reaching a high tier (it's unclear if he landed on 1-B, High 1-B, Low 1-A, or 1-A to me) without mention of infinity, in very narrow cases.
 
Rakih_Elyan said:
Change the FAQ by erasing the notion of accessing 1-A without mention of infinity, since we require it now.
Click to expand...
Agnaa said:
I don't think that's sufficient, since DT is okay with reaching a high tier (it's unclear if he landed on 1-B, High 1-B, Low 1-A, or 1-A to me) without mention of infinity, in very narrow cases.
Click to expand...
@DontTalkDT

What do you think?
 
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