How do we scale this type of infinite iteration?

[DoFliesCallUsWalks]

What interpretation is best for this feat? Basically an infinitely reiterating structure, where Space 1 has a size of infinity to the power of infinity, Space 2 has a size of Space 1 to the power of Space 1, Space 3 has a size of Space 2 to the power of Space 2, etc. What kind of set theory system do we use here, I could do ω but that would scale nowhere, just higher infinite universes that don't even reach low multi.
I think the best way to interpret is interpreting infinity as ℵ0, then the iteration makes sense and is at least functionable. But in that case, the cardinality of 4D or any D or hilbert space are just the same thing, cardinality of the continuum, and it would make Space 1 above hilbert space already, since it's cardinality is ℵ0 to ℵ0, equivalent to 2^ℵ0 and ℵ1, so that makes the first layer already high hyperversal+? I'm completely unsure of where to go here.

 

[DoFliesCallUsWalks]

bump~

 

[DoFliesCallUsWalks]

bump~~~

 

[Tanin_iver]

What interpretation is best for this feat? Basically an infinitely reiterating structure, where Space 1 has a size of infinity to the power of infinity, Space 2 has a size of Space 1 to the power of Space 1, Space 3 has a size of Space 2 to the power of Space 2, etc. What kind of set theory system do we use here, I could do ω but that would scale nowhere, just higher infinite universes that don't even reach low multi.
I think the best way to interpret is interpreting infinity as ℵ0, then the iteration makes sense and is at least functionable. But in that case, the cardinality of 4D or any D or hilbert space are just the same thing, cardinality of the continuum, and it would make Space 1 above hilbert space already, since it's cardinality is ℵ0 to ℵ0, equivalent to 2^ℵ0 and ℵ1, so that makes the first layer already high hyperversal+? I'm completely unsure of where to go here.

It would still be High Hyperversal+, just very high into it.

 

[DoFliesCallUsWalks]

It would still be High Hyperversal+, just very high into it.

Thanks, I figured it was like that. Also, if we interpret infinity here as not aleph null but omega, then the whole structure would be ω↑↑ω, or epsilon naught, which doesn't even get past aleph one?? so what would that make the scaling? can we even use ordinal calculation here?

 

[Tanin_iver]

Thanks, I figured it was like that. Also, if we interpret infinity here as not aleph null but omega, then the whole structure would be ω↑↑ω, or epsilon naught, which doesn't even get past aleph one?? so what would that make the scaling? can we even use ordinal calculation here?

You can list the Ordinal calculation in the Note section, it would be equivalent to epsilon naught dimensions.
High Hyperversal+ and a small citation that leads to the note section.

 

[DoFliesCallUsWalks]

You can list the Ordinal calculation in the Note section, it would be equivalent to epsilon naught dimensions.
High Hyperversal+ and a small citation that leads to the note section.

thanks!