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Math Help - Is this an infinte set?

  1. #1
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    Is this an infinte set?

    True or false. In an infinte metric space, an open ball of radius 2 is an infinte set.

    Well, my answer is false,

    Let M= R.
    Let the metric be given by :
    d(x,y) = 0 if x=y
    d(x,y) = 2 if x<>y

    Then in this metric space, the open ball B[a;r] about a in M has just a single point.

    Is my reasoning right??
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  2. #2
    Super Member redsoxfan325's Avatar
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    Yes.
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