# convex sets

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• October 3rd 2010, 09:20 AM
ekbio
convex sets
prove that the sum and difference of two convex sets in R are convex
• October 3rd 2010, 10:30 AM
Dinkydoe
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...