Math Is Fun Forum

Who eats the pie?

    A,B,C,D and E decide to stop arguing and to do something together for a change. B's Mom bakes them a big pie to celebrate their togetherness. Before they start to eat they begin to argue about primes. They are mathematically inclined after all. They settle down on this one particular question.

    If we start with the set of all fractions with 1 as the numerator and all the primes as denominators ( { 1 / 2, 1 / 3, 1 / 5, 1 / 7, 1 / 11, ...} and each of us starting with A and in order ( A,B,C,D,E, A,B,C,D,E... ) takes the next fraction and eats that amount of the remaining pie. In other words A eats 1 / 2, B eats 1 / 3 of the remaining half, C eats 1 / 5 of the remaining sixth... When we get to E and if there is more pie left we start again with A. The question is will we ever finish the pie?

    A says) Since this can go on forever I think there will always be some pie left.

    B says) Not necessarily sometimes an infinite process can equal a finite number. I think the pie will eventually be consumed.

    C says) Who cares I am hungry.

    D says) No wait, I think I read about something like this called Zeno's paradox.

    E says) Hey D, did you make that up?