- #1

ploppers

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## Homework Statement

Let x* be an element of a convex set S. Show that x* is an extreme point of S if and only if the set S\{x*} is a convex set.

## Homework Equations

(1-λ)x1 + λx2 exists in the convex set

## The Attempt at a Solution

I'm not too sure what S\{x*}, I asssumed it was the same as S/{x*} which is S over {x*}

I have is S?{x*} is a convex set then

λ(K/x*) + (1-λ)(P/x*) is a convex set were K and P are in the convex set S.

[λ(k) + (1-λ)(P)]/x* is in S/{x*}, but I can't see how it must me an extreme point