Notation of set of vectors

Question

I was wondering if someone could clarify this for me. In my lecture notes my lecturer keeps writing "Let $\{\textbf{v}_1,\ldots, \textbf{v}_n\}\in \mathbb{R}^m$ be a collection of vectors $\dots$" and was wondering if this isn't an abuse of notation since each $\textbf{v}_i\in \mathbb{R}^m$ and thus $\{\textbf{v}_1,\ldots, \textbf{v}_n\}\subset \mathbb{R}^m$ as this set itself is not an element of $\mathbb{R}^m$.

Answer 1

Yes, that is abuse of (at least sloppy) notation, for exactly the reasons you gave. Especially so with the set clammers. It would be a lot more acceptable with the more normal:

$$v_1, \dots, v_n \in \Bbb R^n$$