High 1-A/inaccessibility to a hierarchy question

[SubaruN2000]

Let's say a character or realm transcends a R>F hierarchy in a way that they transcend the logical framework of it, see the R>F gaps of the hierarchy as completely meaningless, and is inaccessible to any arbitrary extentions of it no matter how large so that they are tiered as High 1-A.

Can that character or realm be part of a new, different, higher R>F hierarchy thats outside the previous one, even though the gaps between the previous R>F hierarchy are irrelevant to them?

Can the gap between that character/realm and a higher character/realm be equivalent to the gaps between the layers of the R>F Hierarchy that they transcended and still be meaningful?

And would another character being twice (or any finite number of times) as strong as that High 1-A character or character from that high 1-A realm be a contradiction to the R>F layers of the heirarchy they transcended being higher infinities?

 

[ActuallySpaceMan42]

Just because two hierarchies use R > F as a similar method, does not mean that the two R > F methods are equal to one another, as long as that fact is made clear. And no, you can have a High 1-A Character that is x6 stronger than another High 1-B being but still has them exist within the same realm as one another.

 

[SubaruN2000]

But if the high 1-A character transcends the logical framework of the heirarchy to the point that those gaps make no difference to them (in this case being the R>F gaps) then smaller gaps like being finitely stronger should also be meaningless to them too, isn't it? So a finite multiplier of power between that character another character should make no meaningful difference, and if it does, would that not put into question whether the R>F gaps that they trivialize are really higher infinity gaps?

 

[ActuallySpaceMan42]

I don't know what your saying.

 

[SubaruN2000]

Like a character gets high 1-A by exceeding the logical framework of a hierarchy, not just the hierarchy itself. So in the example I provided, a character who gets high 1-A by transcending the logical framework of a R>F hierarchy would be beyond what defines that hierarchy in the first place (i.e. the R>F gaps itself). So those gaps are meaningless to them now, and those R>F gaps are "more than infinitely" stronger by our standards. And that should mean any lesser gap than those gaps is also meaningless. Which would include finite power gaps.

 

[ProfectusInfinity]

Let's say a character or realm transcends a R>F hierarchy in a way that they transcend the logical framework of it, see the R>F gaps of the hierarchy as completely meaningless, and is inaccessible to any arbitrary extentions of it no matter how large so that they are tiered as High 1-A.

So in other words, this verse would have a "no matter the amount of layers added" statement? Statements like that are only high 1-B since infinite layers are already above any countable number. In order to extrapolate that statement to 1-A, you'd need supporting evidence that the hierarchy can be extended infinitely since uncountably infinite layers would then be beyond any countable number. In the case you're decribing, where such a statement qualifies for high 1-A, the number of arbitrary layers that could be added to the hierarchy would have to be equal to aleph infinity. In layman's terms, infinite elements=aleph null, uncountably infinite elements=aleph 1, infinite higher infinities (Infinity^Infinity^Infinity... ad infinitum)=aleph infinity, then beyond all that is the inaccessible cardinal, which can't be reached by accumulating any number of higher infinities.

Aleph null layers/dimensions=High 1-B
Aleph 1 layers/dimensions=Low 1-A
Aleph infinity layers/dimensions=1-A+
Inaccessible cardinal layers/dimensions=High 1-A

Can that character or realm be part of a new, different, higher R>F hierarchy thats outside the previous one, even though the gaps between the previous R>F hierarchy are irrelevant to them?

What do you mean "even though?" All high 1-A hierarchies view a 1-A hierarchy's gaps as irrelevant. What is being contradicted here?

Can the gap between that character/realm and a higher character/realm be equivalent to the gaps between the layers of the R>F Hierarchy that they transcended and still be meaningful?

Technically speaking, the difference between baseline outerversal and a single layer into outer is equivalent to the difference between a normal human and an outerversal character: since each outerversal transcendence is like repeating the whole system of transcendences beneath you. However, most fictions don't treat layers into outer like that, so viewing a 1-A character as fiction should be enough to gain a single layer into outer: even without statements like "he transcends it to the same extent it transcends a human."

On the other hand, if it was stated that the high 1-A hierarchy has layers of transcendence no different from the 1-A hierarchy, that does introduce a problem. I assume that's what you were asking above?

Like I implied before, tiering a single layer into high 1-A means transcending baseline high 1-A to the same extent baseline high 1-A transcends a normal human. Most ficitons don't treat the gap that largely however, so isolated statements of R>F between high 1-A layers should be enough to scale layers into high 1-A. If the high 1-A hierarchy was compared to the 1-A hierarchy not in the sense that they both use R>F transcendences, but specifically that the scope of the inaccessible gap is equal, then yeah, that level of gap isn't inaccessible enough for additional layers into high 1-A.

And would another character being twice (or any finite number of times) as strong as that High 1-A character or character from that high 1-A realm be a contradiction to the R>F layers of the heirarchy they transcended being higher infinities?

Non sequitor? I don't see what's wrong with being twice as strong as a high 1-A character in and of itself? If that character was part of the lower hierarchy, or stated to view the high 1-A entity as fiction, then yeah: that would introduce some contradictions to an R>F level of gap.

 

[SubaruN2000]

What do you mean "even though?" All high 1-A hierarchies view a 1-A hierarchy's gaps as irrelevant. What is being contradicted here?

Yeah so I'm asking if they can be part of a R>F hierarchy even though in order to reach high 1-A they would have to transcend the logical framework of R>F hierarchies, meaning all such hierarchies and gaps are irrelevant them.

If the high 1-A hierarchy was compared to the 1-A hierarchy not in the sense that they both use R>F transcendences, but specifically that the scope of the inaccessible gap is equal, then yeah, that level of gap isn't inaccessible enough for additional layers into high 1-A.

It won't be an additional layer into high 1-A, but can the gap still be applied to those high 1-A characters in a meaningful way? Like if relative gaps to the ones of the 1-A hierarchy they transcend can still apply between those high 1-A characters in a meaningful way. Or if smaller gaps, like being finitely stronger than each other, could apply.

Non sequitor? I don't see what's wrong with being twice as strong as a high 1-A character in and of itself?

But like, if the 1-A R>F gaps, which are supposed to be completely meaningless to them, are equivalent to higher infinity gaps, then smaller gaps like finite gaps should also be of no relevance to them isn't it? So if a high 1-A character is finitely stronger than another one, would that not mean the R>F gaps that are meaningless to them are nor actually infinite gaps?

 

[ProfectusInfinity]

Yeah so I'm asking if they can be part of a R>F hierarchy even though in order to reach high 1-A they would have to transcend the logical framework of R>F hierarchies, meaning all such hierarchies and gaps are irrelevant them.

To put it simply, there's a humongous difference between viewing something baseline 1-A as fiction and viewing something 4-D as fiction. Although both are an uncountably infinite gap, the different measuring sticks they use mean that viewing something 4-D as fiction amounts to a single level of infinity, while viewing something 1-A as fiction is like repeating the whole hierarchy of Infinity^Infinity^Infinity... ad infinitum gaps.

Q: Is transcending an 1-A character to the same degree they transcend normal humans High 1-A?​

A: No. Due to making use of a much larger measuring stick in comparision to lower tiers (Power sets of infinite sets, as opposed to adding individual dimensions), the gap between any two levels in 1-A actually exceeds the entire system below them, and is equivalent to repeating the whole process which led to the previous level on a much higher scale. Thus, most statements that make use of such comparisions would only amount to one further level into the tier, unless some additional context showing it to be higher is present.

The factors aren't what matter. Being twice as strong as someone, infinitely stronger than someone... it's not the factors that determine the degree of inaccessible gap, but the measuring sticks: the tiers that these factors are applied to. Take 3 as a measuring stick, then multiply 2: that's a +3 gap. Take 10 as a measuring stick, then multiply 2: that's a +10 gap. 20 transcends 10 the same way 6 transcends 3 when we look at pure factors, but fundamentally speaking, the level of inaccessible gap is larger with the latter since it uses a greater measuring stick.

I hope that answers your questions.