# Need help understanding convex sets

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?

Tags :

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.