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Thread: The continuity of f(x,y)=x+y

  1. #1
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    The continuity of f(x,y)=x+y

    I want to check, using the epsilon-delta-definition of continuity, that the function f(x,y)=x+y is continuous. But I can't seem to find a way to show that for epsilon > 0, sqrt((x-x')^2+(y-y')^2) < delta implies |x + y - x' - y'| < epsilon. Any help?
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  2. #2
    Senior Member roninpro's Avatar
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    Did you think about using some equivalent metrics? The taxicab metric seems to do the trick.

    If you're unfamiliar, it is

    $\displaystyle \rho((x_0,y_0),(x_1,y_1))=|x_0-x_1|+|y_0-y_1|$.

    Good luck.
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