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    Hello there, I am just having a little difficulty verifying whether or not the following is a metric on R^2. (I am finding it difficult to show that all the 4 properties of a metric space hold.)

    "d(x,y) = |x_1| + |y_1| + |x_2| + |y_2|"

    Any help would be much appreciated. Thank you for your time
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    Not a metric space because x = y doesn't imply d(x, y) = 0.
 
 
 
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Updated: January 31, 2006

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