A dog has infinitely many pieces of meat, but on each piece of meat there is a fly. At each move, the dog does the following:[*] He eats a piece of meat together with all flies lying on it;
[*] He moves a fly from a piece of meat to another.The dog doesn't want to eat more than one milion flies. Prove that he cannot ensure that each piece of meat is eaten at some point.Proposed by I. Mitrofanov