If I want $x_i$ to be an arbitrary element of a vector $\vec{x}$ can I use the following notation: $x_i \in \vec{x}=[x_1\;x_2\;\cdots\;x_n]^T\in \mathbb{R}^n$? And if I later want to specify the interval of each $x_i$ to be between $0$ and $1$, can I then say that $x_i \in [0,1]\;\forall i$? Is this mathematically correct usage of $\in$ for both cases?
The actual problem I have is that I want to say that $y_i\in\vec{y}$ for $i\in\{1,2,\cdots,n\}$ and that each $y_i$ is binary $y_i\in\{-1,+1\}$. Should I stick to something like $\vec{y}\in\{-1,+1\}^n$ instead?