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Math Help - Infinity problem- possible or not?

  1. #1
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    Infinity problem- possible or not?

    A long row of people (infinitely many of them!) each have $1 (in one coin, note or whatever you use in your countries). Each person is in a numbered seat, starting with seat 1. They want to redistribute the money so that each person in the row has more money than the previous person. How can they do this?
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  2. #2
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    Quote Originally Posted by ljonz View Post
    A long row of people (infinitely many of them!) each have $1 (in one coin, note or whatever you use in your countries). Each person is in a numbered seat, starting with seat 1. They want to redistribute the money so that each person in the row has more money than the previous person. How can they do this?
    As we have only $1 notes which cannot be subdivided the person in seat n can have $n ($(n-1) also works as does the n-th term of any strictly increasing integer sequence). Is there enough money to do this? Why yes since we start with an infinite total, and we still have an infinite amount afterwards.

    Think of it like this, the 1st person keeps their dollar, the next person keeps their dollar and takes the dollar from the next person.

    We continue with the next person who has not yet recieved their total (in seat n) taking n dollars from the next n persons that have any, and so on.

    It is a bit like a chain letter but with an infinite population, so you never run out of new money.

    This is a variant on Hilbert's Hotel.

    RonL
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  3. #3
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    Wow, that was fast!

    Cheers Ron L! Now that you've described it, it seems so simple.
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