Lbh pna'g unir nyrcu-bar phorf orpnhfr rnpu phor zhfg pbagnva ng yrnfg bar cbvag jubfr nyy guerr pbbeqvangrf ner engvbany, naq gurer bayl ner nyrcu-mreb fhpu cbvagf.
[This comment is no longer endorsed by its author]Reply
1MrMind
This is the 3D version of the countable antichain condition (commonly known as c.c.c.).
c.c.c. is implied by a property called separability, which is part of the definition of the real line (the unique linear complete separable order).
So you can fit aleph1 "cubes" only if you operate in a modified notion of space which is not c.c.c.
On the other hand, the real line contains aleph1 points only in some model of set theory. The precise quantity is 2^aleph0.
0Gurkenglas
Given aleph-one cubes with no common volume in 3D space, replacing each cube with the largest sphere that fits in it will give you aleph-one spheres with no common volume in 3D space.
If it's worth saying, but not worth its own post, then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should start on Monday, and end on Sunday.
4. Unflag the two options "Notify me of new top level comments on this article" and "