>>68
Like the Banach-Tarski Theorem, which postulates that given single orange you can transform it into two oranges, by the sole power of applying Set Theory axioms. Behold The Wonder of Infinity's Creation!
Also worth noting that those apples are nothing like our apples. Our apples are made of finite atoms occupying finite space and that you can't really divide them too much (up to subatomic particles, although thinking of them like that might be wrong). On the other hand, a "set theory" sphere can be cut with infinitely precise detail, that is, it would take infinite bits to specify where you want to cut (that's a real for you) and how. This obviously wouldn't work with a finitely detailed apple (or one which only works with rationals, which still allow for unbounded "detail").
tl;dr: Set theoretical universe sphere != physical sphere made of atoms.