 In the traditional cut-and-choose game you take a piece of cake and cut it into two smaller pieces; then I choose one of the pieces and eat it, leaving the other one for you. This procedure is supposed to put pressure on you to cut the cake fairly. Mathematicians, not quite understanding the purpose of the exercise, insist on iterating it. Thus I make you cut the piece I chose into two, then I choose one of those two; then you cut this piece again, and so on indefinitely. Some even more unworldly mathematicians make you cut the cake into countably many pieces instead of two. 