I have to prove or disprove that {x ∈ $\mathbb{R}^n$: $\sum_{i=1}^n x_i^2 = 1$} is convex.
I don't even understand what kind of set this is, i.e. which values of $x$ are in this set.
I know that I gotta use the following for a prove:
A set $\Omega \subset \mathbb{R}^n$ is convex if $ \alpha x+(1−\alpha)y \in\Omega,∀x,y \in\Omega$ and $∀ \alpha ∈[0,1]$.
But maybe a disprove would be easier?