Splitting an infinite set into two equal infinite subsets.
and B and C must be disjoint.
A=Integers: B= even integers, C=odd integers. Done.
A=Reals: B=(-infinity,0), C=[0, infinity). Done.
A=P(R): B=? C=? The problem begins with cardinality greater than c.
How about this: Well-order A. Put the first element in the left bin, the second in the right bin,...alternatingly put the elements of A
in the left bin and right bin. By transfinite induction, this can be done for all elements of A. Then each bin has |A| elements.