# Notation of set of vectors

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 $\mathbb{R}^m$.

• Yes, it's an abuse of notation (for the reason you gave). – Daniel Fischer Mar 22 '14 at 15:39
• Too much abuse, to be honest. – Git Gud Mar 22 '14 at 15:40

$$v_1, \dots, v_n \in \Bbb R^n$$
• Another reason for not writing the set brackets is that one often doesn't want to exclude the possibility that some of the $v_i$s are equal. – Henning Makholm Mar 22 '14 at 16:11