For a function $f: \mathbb{R}^n \to \mathbb{R}^m$, strictly speaking, is it abuse of notation/incorrect to write "$f(x_1,x_2,\ldots,x_n) = f(\mathbf{x})$ where $\mathbf{x} = \langle x_1,x_2,\ldots,x_n \rangle$"? This notation is commonplace, but it seems incorrect to me since the domain of $f$ is $\mathbb{R}^n$, which is just the $n$-fold Cartesian product of $\mathbb{R}$ with itself and is not a set of vectors (apologies if there is no such thing as a "set of vectors" or if such a term is ambiguous, I'm just a humble Calc III-let). Does it turn out that every element of $\mathbb{R}^n$ is actually a vector and I'm fucking up? This also seems incorrect.