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Math Help - convex sets

  1. #1
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    convex sets

    prove that the sum and difference of two convex sets in R are convex
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  2. #2
    Senior Member Dinkydoe's Avatar
    Joined
    Dec 2009
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    Just work from the definitions: If R is convex then for any x,y\in R we have that any convex combination \lambda x+(1-\lambda)y is element of R, with \lambda\in [0,1]

    Now you need to show for 2 convex sets R_1,R_2 that,

    if x_1,x_2\in R_1, y_1,y_2\in R_2 then \lambda (x_1+y_1)+(1-\lambda)(x_2+y_2) is element of  R_1\oplus R_2

    The difference is actually the same excercise...
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