Given aleph-one cubes with no common volume in 3D space
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?
Others are telling me, not to even try, because it’s surely impossible and I will suffer some great misfortune, if I try.
No one is telling Thomas that he will suffer any great misfortune if he tries, beyond the misfortune of almost certainly wasting his time.
Thomas, you made a similar claim earlier and I explicitly rejected it and reiterated that if you choose to go looking for mathematical contradictions I wish you well. Why are you telling untruths about other people? I think that’s rude.
Now, what if we have countably infinite amount of space dimensions. How many (rational) points are there?
Continuum-many, because e.g. any sequence of 0s and 1s corresponds to an integer (hence rational) point in aleph0-dimensional space. And you can put a side-1/2 cube around each of them to get continuum-many disjoint hypercubes in that space. The cardinality of the space itself is continuum^aleph0 = continuum, so in this case you have as many disjoint hypercubes as points.
(None of this is difficult, controversial, contradictory, or indicative of any sort of inconsistency.)
Aleph-zero dimensions give you aleph-one (=continuum) rational points. And also aleph-one hypercubes.
Since those two numbers are equal, this is not a way to reproduce a paradox in such a space.
Fine, no problem, just another rock with no snake under it. In other words, the ZF has survived another test, as it has survived one billion or so tests before.
As long as you believe, the Yablo’s paradox has nothing to do with the ZF, that it is completely isolated from the ZF, then we have no case against ZF, whatsoever.
Well, I don’t, you guys do believe that the semantics Yablo used, cannot be used against the ZF.
I think that this is a correct and honest description of our disagreement.
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?
No one is telling Thomas that he will suffer any great misfortune if he tries, beyond the misfortune of almost certainly wasting his time.
Thomas, you made a similar claim earlier and I explicitly rejected it and reiterated that if you choose to go looking for mathematical contradictions I wish you well. Why are you telling untruths about other people? I think that’s rude.
Continuum-many, because e.g. any sequence of 0s and 1s corresponds to an integer (hence rational) point in aleph0-dimensional space. And you can put a side-1/2 cube around each of them to get continuum-many disjoint hypercubes in that space. The cardinality of the space itself is continuum^aleph0 = continuum, so in this case you have as many disjoint hypercubes as points.
(None of this is difficult, controversial, contradictory, or indicative of any sort of inconsistency.)
Let us stick to the essentials here.
Aleph-zero dimensions give you aleph-one (=continuum) rational points. And also aleph-one hypercubes.
Since those two numbers are equal, this is not a way to reproduce a paradox in such a space.
Fine, no problem, just another rock with no snake under it. In other words, the ZF has survived another test, as it has survived one billion or so tests before.
As long as you believe, the Yablo’s paradox has nothing to do with the ZF, that it is completely isolated from the ZF, then we have no case against ZF, whatsoever.
Well, I don’t, you guys do believe that the semantics Yablo used, cannot be used against the ZF.
I think that this is a correct and honest description of our disagreement.