Question about dimensional tiering

[Panpanpanjeidj]

In dimensional stratification, one~aleph1 dimensions have the same cardinality.

However, the reason why higher dimensions can have an infinitely larger volume than lower dimensions is probably because of the concept of separate size given to each dimension.

In this case, if 0 dimension is aleph0, is 1 dimension aleph1 and 2 dimension aleph1×aleph1?

If so, wouldn't Low 1-A be aleph2 because it becomes aleph1^aleph1?

 

[GreatIskandar14045]

Infinite*infinite isn't higher infinity, it is still has the same cardinality as the smallest infinity, because you can do one to one correspondence from one to another (bijection), like, the set of rational numbers (all fractions that can be expressed by ratio) to natural numbers (all positive numbers) via cantor's diagonal argument (see this video for better explanation, I've timestamped it), both of them are aleph-0 and have the same size.

Infinite^(infinite) or the power set of infinity or P(aleph-0) is uncountable, and is equal to 1 dimension (I will elaborate why on the next comment if you still want me to explain it, no worries).

And aleph-1 is 1 dimension in this site.
Anyway, don't ever think about aleph-1 is equal to 1 dimension in general insight, aleph-1 = 1 dimension is based on continuum hypothesis which couldn't be proven nor disaproven.