is a cube (since it will have no empty spaces).
It’s not a cube. The corner points for example, are NOT covered by any sphere. Its a cube MINUS infinitely many points.
On the edges, for example, only aleph zero points are covered and aleph one many—aren’t.
The limit technique you employ here, does not apply at all.
Thank you I fixed it. I think the same argument shows that that question is also undefined. I think the real takeaway is that physics doesn’t deal well with some infinities.
The question may be flawed in a way that I don’t see it.
Or the question may be flawed not by my mistake, but by a mistake already built in R^3 or R^4 math.
I think, it’s the later.
It’s not a cube. The corner points for example, are NOT covered by any sphere. Its a cube MINUS infinitely many points.
On the edges, for example, only aleph zero points are covered and aleph one many—aren’t.
The limit technique you employ here, does not apply at all.
Thank you I fixed it. I think the same argument shows that that question is also undefined. I think the real takeaway is that physics doesn’t deal well with some infinities.
The question may be flawed in a way that I don’t see it.
Or the question may be flawed not by my mistake, but by a mistake already built in R^3 or R^4 math.
I think, it’s the later.