Closedness of a set I am trying to understand closed sets.
Is the set
$$
A =\{x \in \mathbb{R}^2: \lVert x \rVert_2 \leq 1 \} -\{0\}
$$
closed?
I think it is not, because if we take the sequence $(\frac{1}{n})_{n=1}^{\infty}$ we can see it lies in A, but its limit is zero which is not in the set A. And because of that, A is not a closed set.
Is this right? Thank you.

It is almost correct, but you missed the fact that $(\forall n\in\Bbb N):\frac1n\notin\Bbb R^2$. Take the sequence $\left(\left(\frac1n,0\right)\right)_{n\in\Bbb N}$ instead.
