> It relies on uncountably-infinite division of an object
But the theorem claims finite division and not infinite?
In R³, given a solid ball B of radius R
it is possible to partition B into finitely many
pieces such that those pieces can be reassembled
to form two solid balls B1 and B2 each of
radius R
Finitely many pieces, but on infinitely variable boundaries. It was clever to make the proof allow a finite number in that place. Without, it would have attracted no attention.
But the theorem claims finite division and not infinite?
In R³, given a solid ball B of radius R it is possible to partition B into finitely many pieces such that those pieces can be reassembled to form two solid balls B1 and B2 each of radius R