by Ash
Last Updated October 09, 2019 21:20 PM

Is it wrong for me to associate a set being convex as a set being closed under addition and multiplication?

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.

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