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Unfortunately we don't know how to fill aleph-one cubes into 3D space in a way, that they don't overlap with 3D intersections.
We can easily do so with aleph-zero cubes, but have no known way to do it with aleph-one cubes.
Others are telling me, not to even try, because it's surely impossible and I will suffer some great misfortune, if I try.
I am not sure, if it's really impossible.You can surely fil N dimensional hyperspace with aleph-one N-1 dimensional hypercubes. That IS possible.
Now, what if we have countably infinite amount of space dimensions. How many (rational) points are there? And how many countably infinite dimensional hypercubes we can squizz there?
I don't know, but it's possible to calculate and to see how the ZF would handle that.
The first sentence of your post on protokol2020 is "There are at most aleph-zero disjunct 3D spheres in 3D space.", so I gave a way to make aleph-one spheres from aleph-one cubes, in order to disprove the possibility of aleph-one cubes.
Aleph-zero-dimensional space has aleph-one rationals. Note that the union of all finite-dimensional spaces (each embedded in the next as a slice) has aleph-zero rationals.
Science demands that you notice an anvil dropped on your head, and my heuristics are also saying you're turning into a math crank.
Then again, if in all spacetime there's one Jesus and a million madmen believing they're Jesus, would we rather that they all believe themselves madmen?