Proving a noSet is Convex

Hi there

How would I go about proving that "S= (x1,x2): x1 + x2 ≤ 1 , x1 ≥ 0)" is a convex set?

Thanks

*Sorry for the title typo

Quote:

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Originally Posted by Lior539

Hi there

How would I go about proving that "S= (x1,x2): x1 + x2 ≤ 1 , x1 ≥ 0)" is a convex set?

Thanks

*Sorry for the title typo

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Take any two points ; you must prove that :

, and now you have the simple task yo show that:

1) ;

2) ...(Happy)

Tonio

Thanks for your help Tonio, it really cleared up some things in my mind. How would one go about proving (1) and (2) though?

Thanks :)