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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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What is the locus defined by those equations?

I would like to know what is the locus of $x \in \Bbb R_+^n$ ($n=2$ would already be fine) defined by $\sum a_i \cdot x_i$ s.t. $a_i+\epsilon \geq 0$, $\epsilon \in \Bbb R$. I know that if $\epsilo …
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