Convex Sets

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Convex Set

A set [math]S[/math] is said to be convex if whenever two points [math]x[/math] and [math]y[/math] are in the set [math]S[/math] then all the points on the line segment joining [math]x[/math] and [math]y[/math] are also in the set [math]S[/math].

A set [math]S[/math] is said to be convex if for [math]x[/math] and [math]y[/math] in [math]S[/math] and [math]\lambda[/math] is a real number such that [math]0\lt\lambda\lt1[/math], then [math]\lambda x+(1-\lambda)y[/math] always belongs to the set [math]S[/math].

A convex set is always a closed set with bulging boundaries.


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