It is mentioned that we can only separate two convex sets only when at least one is bounded (compact). Now if we take epigraph of $f(x) = x^2 +1$ and the other is below the $x$ axis, I can find a function $f(x)=0.5$ that can separate these two epigraphs which are convex and unbounded. Please help me to understand where I am wrong in my understanding?
2026-05-05 14:44:44.1777992284
Strictly seperating convex sets if one of the two is bounded?
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