Is it wrong for me to associate a set being convex as a set being closed under addition and multiplication?
2026-04-09 14:55:55.1775746555
Need help understanding convex sets
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Every subset of $\mathbb R^n$ which is closed under addition and multiplication by scalars is convex. However, there are much more convex sets than that. For instance, a closed disk in $\mathbb R^2$ is convex, but it is neither closed under addition nor under multiplication by scalars.