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Math Help - This seems impossible (metric space distances)

  1. #1
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    This seems impossible (metric space distances)

    So, in a metric space, we define a distance function as D --> R+ union {0}.

    Now, there's a problem in my book where the assumption says

    For 0 <= x < 1, there's a distance (for a sequence) such that d(n+1, n+2) < (x) d(n, n+1).

    So, for the case where x = 0, we have that d(n+1, n+2) < 0.

    I don't see how this is possible.
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  2. #2
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    Quote Originally Posted by Chizum View Post
    So, in a metric space, we define a distance function as D --> R+ union {0}.

    Now, there's a problem in my book where the assumption says

    For 0 <= x < 1, there's a distance (for a sequence) such that d(n+1, n+2) < (x) d(n, n+1).

    So, for the case where x = 0, we have that d(n+1, n+2) < 0.

    I don't see how this is possible.
    That isn't possible. A "distance" is never negative. Perhaps you have misread it.
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