I am working with discrete sets but I have a doubt: is the set $\{ 0,1\}$ compact and convex? And the set $\{ 0,1\}^2=\{(0,0), (1,0), (0,1), (1,1) \}$?
2026-04-01 21:52:55.1775080375
Compact and convex discrete set
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$\left \{0,1\right \}$ is not convex, because based on defintion $\lambda*0+(1-\lambda)*1 \notin \left \{0,1\right \}$.