Why aleph 2 or 3 is outerversal

[Fixxed]

Why aleph 2 or 3 get outerversal level by default???

We currently gave aleph 2 number of everything (exluding dimension) a low 1A rating, and aleph 3 number of everything even a grain of sand a 1A rating

 

[ActuallySpaceMan42]

No, we don't.

An Aleph-Null amount of sand is High 3-A, an Aleph-1 is Low 2-C, and an Aleph-3 amount is Low 1-C, so on and so forth up to High 1-B.

An Aleph-Null of Universes is 2-A, and Aleph-1 of Universes is Low 1-C, and so on and so forth up to High 1-B.

 

[Fixxed]

No, we don't.

An Aleph-Null amount of sand is High 3-A, an Aleph-1 is Low 2-C, and an Aleph-3 amount is Low 1-C, so on and so forth up to High 1-B.

An Aleph-Null of Universes is 2-A, and Aleph-1 of Universes is Low 1-C, and so on and so forth up to High 1-B.

No, aleph 2 number of whatever element is that is low 1A by default

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.

 

[ActuallySpaceMan42]

No, aleph 2 number of whatever element is that is low 1A by default

Whoever told you that is wrong then.

 

[Oblivion_Of_The_Endless]

Whoever told you that is wrong then.

It's from the FAQ...

 

[ActuallySpaceMan42]

It's from the FAQ...

---

This can be extrapolated to larger cardinal numbers as well, such as aleph-3, aleph-4, and so on, and works in much the same way as 1-C and 1-B in that regard.

It's literally stated that 1-A can be extended using Alephs, just like 1-C can be extended to 1-B.

Characters or objects that can affect structures with a number of dimensions greater than the set of natural numbers, meaning in simple terms that the number of dimensions is aleph-1 (An uncountably infinite number, assumed to be the cardinality of the real numbers themselves)

Low 1-A is effecting an uncountably infinite number of dimensions, meanwhile Low 1-C.

Characters or objects that can universally affect, create and/or destroy spaces whose size corresponds to one to two higher levels of infinity greater than a standard universal model (Low 2-C structures, in plain English.)

In terms of "dimensional" scale, this can be equated to 5 and 6-dimensional real coordinate spaces (R ^ 5 to R ^ 6)

Is affecting a higher level of infinity, and they specifically use R^5 as an example, with real numbers being the cardinality of uncountable infinity, also known as Aleph -1.

aleph-1 (An uncountably infinite number, assumed to be the cardinality of the real numbers themselves),

So no, whoever told him that is wrong, and if it's on the FAQ then it's a contradiction.

 

[Oblivion_Of_The_Endless]

It's literally stated that 1-A can be extended using Alephs, just like 1-C can be extended to 1-B.

"just like 1-C can be extended to 1-B" is to reference that each aleph would be a layer higher into 1-A (aleph-3 dimensions would be one layer above baseline, aleph-4 would be two layers above baseline, and so on), but thats not the case with the tiers lower. Since, for example, an aleph-1 amount of breads would be Low 2-C while an aleph-1 amount of dimensions is Low 1-A. It depends on what you apply Aleph-1 quantity into (all the tiers from 11-B to Low 1-A are applications of Aleph-1, such as R^1, R^2, R^3, R^4, etc). But when it comes to aleph-2 and higher, it isn't, since even the lowest application of Aleph-2, such as R^R^1, is still R^R and thus already bigger than anything else Aleph-1 could offer.

So no, whoever told him that is wrong, and if it's on the FAQ then it's a contradiction.

It indeed is on the FAQ

 

[ActuallySpaceMan42]

It indeed is

Oh, it's R^Number, not R^R, I'm stupid, never mind.

Thanks for letting me know.

 

[Hjxdvd]

Aleph 1 isn’t a set, it’s a cardinality. So the power set of it doesn’t make sense. Aleph 2 is the smallest cardinal larger than aleph 1. Aleph 2, according to GCH, is the cardinality of the power set of a set with cardinality aleph 1

Regardless of the fact that ChatGPT is bad for math, it is not correct to say in general that |2^R| is aleph_2. This is only true if you assume a stronger version of the continuum hypotheses (you don't need the full "generalized continuum hypothesis", but this does not follow afaik from the continuum hypothesis alone). The CH and GCH are independent of the usual axioms we take in math (they are extra assumptions you can add), so don't think of |2^R| as aleph_2 or |R| as aleph_1, but rather think of |2^R| as |2^R| and |R| as |R| (or |2^N|)

 

[Fixxed]

Aleph 1 isn’t a set, it’s a cardinality. So the power set of it doesn’t make sense. Aleph 2 is the smallest cardinal larger than aleph 1. Aleph 2, according to GCH, is the cardinality of the power set of a set with cardinality aleph 1

Cardinality is the size of the set bruh

 

[Greatsage13th]

Would cardinals still be above alephs in general?

 

[Fixxed]

Would cardinals still be above alephs in general?

Cardinal is size of set (whatever set is that). That universal bruh... not in hierarchy of infinities

Btw aleph is small cardinal, beyond that is large cardinal. But you can have cardinal with just a finite set

 

[Hjxdvd]

Cardinality is the size of the set bruh

Reading comprehension devil strike again.

Would cardinals still be above alephs in general?

If pressed for a yes or no answer I would say the aleph_0 is a limit cardinal, yes: the set of all smaller cardinals doesn't have a largest element.

Then the first unambiguously limit cardinal (if we don't count aleph_0) would be aleph_omega, after which aleph\_(omega+1) is again a successor cardinal.

Fun Fact: It probably doesn't help that it is comparatively complicated to explain what aleph_1 actually is the cardinality of. "The set of isomorphism classes of well-ordering relations on N" sure, but there's a lot of explanation to unpack there.

 

[Fixxed]

Reading comprehension devil strike again.

Where you get, aleph 1 isnt a set?