Why does p(p(ℵ0)) grant h1B+ even if its just points or universes?

[eternal1234]

So i have a big doubt regarding a statement from this page:

Tiering System FAQ

A: Whether higher-dimensional entities qualify for such high tiers or not depends on several different factors, which may take root both in and out-of-verse. To explain this situation, we must first clarify what exactly being higher-dimensional entails. In a way, yes, though not how most would...

vsbattles.fandom.com

Which is:

However, the same does not apply to 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 (Points, universes, dimensions, etc). From this point and onwards, all such sets are High 1-B+

Assuming continuum hypothesis as true(since p(ℵ0) is also taken as ℵ1) wouldn't p(p(ℵ0)) just be ℵ2?

Since p(ℵ0) is 2^ℵ0 which is ℵ1, so p(p(ℵ0)) would just Be 2^ℵ1 which would be ℵ2?

And shouldn't that amount of universes be 6D since ℵ1 universes is 5D?

 

[SweetDao]

Since p(ℵ0) is 2^ℵ0 which is ℵ1, so p(p(ℵ0)) would just Be 2^ℵ1 which would be ℵ2?

Yes.

And shouldn't that amount of universes be 6D since ℵ1 universes is 5D?

No, because that amount of universes (or anything, really) would be greater than what the real coordinate space could potentially hold.

If you imagine the real coordinate space as a box where you can put anything inside of it (universe, atoms, buildings,...) a number of universes equal or greater than aleph 2 would be so large that it wouldn't be able to fit into that box. The content would spill out of it, even if it's just regular 3D universes, making it therefore bigger than the upmost limit of that box (High 1-B+).

 

[eternal1234]

Yes.



No, because that amount of universes (or anything, really) would be greater than what the real coordinate space could potentially hold.

If you imagine the real coordinate space as a box where you can put anything inside of it (universe, atoms, buildings,...) a number of universes equal or greater than aleph 2 would be so large that it wouldn't be able to fit into that box. The content would spill out of it, even if it's just regular 3D universes, making it therefore bigger than the upmost limit of that box (High 1-B+).

I see

 

[eternal1234]

Yes.



No, because that amount of universes (or anything, really) would be greater than what the real coordinate space could potentially hold.

If you imagine the real coordinate space as a box where you can put anything inside of it (universe, atoms, buildings,...) a number of universes equal or greater than aleph 2 would be so large that it wouldn't be able to fit into that box. The content would spill out of it, even if it's just regular 3D universes, making it therefore bigger than the upmost limit of that box (High 1-B+).

So Basically it goes like this?

for a infinite 3D space all possible points are the all possible combinations of 3 unique coordinate points (x, y, z) over an infinite space which would be 3^ℵ0 which would be ℵ1


Same for 4D space: 4^ℵ0 = ℵ1
And for 5D space: 5^ℵ0 = ℵ1
And so on
until you reach ℵ0D: where ℵ0^ℵ0 also equals ℵ1


And ℵ2 amount of anything will still keep going on after that hence h1B+?

 

[SweetDao]

So Basically it goes like this?

for a infinite 3D space all possible points are the all possible combinations of 3 unique coordinate points (x, y, z) over an infinite space which would be 3^ℵ0 which would be ℵ1


Same for 4D space: 4^ℵ0 = ℵ1
And for 5D space: 5^ℵ0 = ℵ1
And so on
until you reach ℵ0D: where ℵ0^ℵ0 also equals ℵ1


And ℵ2 amount of anything will still keep going on after that hence h1B+?

I'm unsure about your explanation, but basically ℵ2 amount of anything would be strictly greater than anything below it, in this case, even an infinite-dimensional space.

 

[eternal1234]

I'm unsure about your explanation, but basically ℵ2 amount of anything would be strictly greater than anything below it, in this case, even an infinite-dimensional space.

Aight