Show that any ball (open or closed) in $\mathbb{R}^n$ is a convex set.

Asked Aug 21 '18 at 16:36

Active Aug 21 '18 at 16:48

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I tried to show that the set $X = \{(x, y)\in \mathbb{R}^2 : x^2 + y^2<1\}$ is convex.

edited Aug 21 '18 at 16:48

Taroccoesbrocco

asked Aug 21 '18 at 16:36

Rogerio Soares

So? How did you start? – amsmath Aug 21 '18 at 16:38
1

Do you mean $x^2+y^2<1$? Because $(1,1), (-1,-1)\in X$ but the line connecting them is not. – cansomeonehelpmeout Aug 21 '18 at 16:39
really, I realized that it does not make sense what I wrote, I have no idea where to start. – Rogerio Soares Aug 21 '18 at 20:15
I'm hopeless in this demonstration. Could someone help? – Rogerio Soares Aug 21 '18 at 21:20

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