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## Homework Statement

Prove that the intersection of a number of finite convex sets is also a convex set

## Homework Equations

I have a set is convex if there exists x, y in the convex S then

f(ax + (1-a)y< af(x) + (1-a)y

where 0<a<1

## The Attempt at a Solution

i can prove that

f(ax + (1-a)y) < f(x) given that x is a global minimizer

then i guess that i could find another arbritary point close to x , x_1, x_2 and add their given function satisfying the convex condition to get

Sum f(axi + (1-a)y) < Sumf(xi) where i= 1, 2,...n

any help would be appreciated