Tiering an Infinite Hotel?

[Flashlight237]

So, a common paradox is the one involving a hotel with infinite rooms, which is used to explain how impossible it is to really perceive infinity. These two videos explain it best:




Under our current tiering system, what tier would we need to truly fill an infinite hotel?

 

[Thelastmlg]

high 3-A hax, infinite speed and AP if you made the hotel or the people within

 

[Flashlight237]

high 3-A hax, infinite speed and AP if you made the hotel or the people within

That is possible, but then again, apparently an infinite hotel can hold an infinite amount of people from an infinite amount of infinitely-long buses (the means of doing so being described in the videos provided), which makes things weirder imo.

 

[Tanin_iver]

That is possible, but then again, apparently an infinite hotel can hold an infinite amount of people from an infinite amount of infinitely-long buses (the means of doing so being described in the videos provided), which makes things weirder imo.

Infinity can have subsets that have infinite size and the same cardinality. For example, the sets of even integers and odd integers are just subsets of the set of integers, yet they are infinite in size and have the same cardinality.
Even the description about infinite number of infinitely long buses can be defined in the same way using subsets of other larger set while having the same cardinality.

 

[Flashlight237]

Infinity can have subsets that have infinite size and the same cardinality. For example, the sets of even integers and odd integers are just subsets of the set of integers, yet they are infinite in size and have the same cardinality.
Even the description about infinite number of infinitely long buses can be defined in the same way using subsets of other larger set while having the same cardinality.

That is true, but at the same time, the wiki's a little weird in that regard and we basically count layered infinities as other tiers entirely (ex. Low 1-C for two layers of infinity), and we even consider Aleph-0 as Low 1-A or 1-A for some reason (even when the 2nd video provided an explanation as to what Aleph-0 is).

 

[Tanin_iver]

That is true, but at the same time, the wiki's a little weird in that regard and we basically count layered infinities as other tiers entirely (ex. Low 1-C for two layers of infinity), and we even consider Aleph-0 as Low 1-A or 1-A for some reason (even when the 2nd video provided an explanation as to what Aleph-0 is).

The wiki treats higher infinities as higher tiers or structures. Infinite planets (Aleph-0) will be High 3-A.

Uncountable infinite (Aleph-1) Snapshots of a Universe (basically a timeline) is Low 2-C which is a higher dimension.
Aleph-1 universes is Low 1-C and Aleph-1 dimensions is Low 1-A.

Just to be clear Aleph-0 dimensions is High 1-B while Aleph-2 dimensions is 1-A in the wiki.

The Hilbert Hotel is defined on countable infinity which has Aleph-0 size, which can be easily defined in High 3-A, while the Bus with people named using an infinite string of A and B is a greater infinity of size Aleph-1 so if we had to tier that, it will be Low 2-C.

For even bigger infinities it will just keep increasing in dimensionality.

EDIT: Also, Large Size Type 8 for Hilbert Hotel

 

[Greatsage13th]

Low 1-C at most