Highlights
I don't really understand the question but lemme get this clear, aleph-1 is Low 1-A and aleph-n (or aleph-infinite/aleph-omega, preferably) is 1-A+. If I'm not mistaken with your question, you're saying that aleph-1 is Low 1-A and aleph-2 is 1-A+, so on.
But that's not how it works, I'll explain this in layman's terms, that higher aleph numbers would transcended the lower numbers on the entirety like higher and lower dimensional difference or say, all levels transcendence, at least that's how higher infinities works in this site (this site seems used continuum hypothesis as true, it is the hypothesis which asserted that aleph-1 = 1 dimension).
Aleph-0 is the smallest infinity aka 0D, aleph-1 is 1D, aleph-2 is 2D, and so on until aleph-n which is infinite D.
So by using the topology of dimensions as the elements it would be:
Aleph-0 is High 1-B or infinite dimensions, aleph-1 is Low 1-A, and so on until aleph-n which is 1-A+.
Where the hell did you learnt all of these? If you know how countably infinite works then you're aware that adding 1 to infinity or infinite+1 would still results the same cardinality, infinite+1 is infinity, infinite+infinite is infinity, even infinite*infinite is still baseline infinity, because bijection (one to one correspondence) exist, that you can biject the set of naturals or N (infinite) to the set of integers or Z (infinite+infinite), like:
N = 1, 2, 3, 4, 5... infinity
Z = 0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5.... infinity
Thus, they have the same size. You can even biject infinite to infinite*infinite, or N to Q (the set of rationals) with Cantor's diagonal argument, because you need exponentiation and power set in order to reach higher infinity. So there's no such thing as aleph x+1 via your definition, at least. In order to see aleph-2 as nothing but fiction, you need aleph-3, which will correspond to 2D and 3D.
First of all, this is the very first time that I heard "aleph 2+1", I believe such thing doesn't exist or either way you're literally refering to aleph 3 just like how the dimensions of 3+1 (like 3 dimensions of space being intertwined with 1 dimension of time) is 4D.
And... that's not how it works, because said logic can also be applied to dimensional space that you can't reach higher dimension just by stacking infinities, since higher dimensional space (in comparison to lower dimensional space) isn't just infinitely larger, it is uncountably infinitely larger because the set of real numbers (with the notation of R) which presented as the line of 1 dimension (1 dimension is a length, 2 dimensions are length and width) is uncountable, and aleph-1 is the first uncountably infinite.
Aleph-1 = 1 dimension (assuming that the continuum hypothesis is true), so saying that aleph-2 is 1-A+ is just like saying that the next level of reality transcendence of 1-A or say, 2x 1-A is equal to 1-A+. It doesn't make any sense, as there is no story that aleph-2 > 3 dimensions mathematically-wise, 1 dimension can only be larger or equal to aleph-1.
Collect and share the web
Get started for free