When using the convention making a label bold to indicate a vector, should you still use the bold if you are only referring to a single element of the vector?
for example, which of these methods of notation would be considered more correct?
eg. 1:
\begin{equation*}
\begin{aligned}
& \text{maximise}
& & \mathbf{x}^2 \\
& \text{subject to}
& & 3x_1 + 2x_2 \leq 6\\
& & & -3x_1 + 2x_2 \leq 0\\
& & & x_k \in \mathbb{Z}, & k \in \{1, 2, \dots, |\mathbf{x}|\}\\
\end{aligned}
\end{equation*}
eg. 2:
\begin{equation*}
\begin{aligned}
& \text{maximise}
& & \mathbf{x}^2 \\
& \text{subject to}
& & 3\mathbf{x}_1 + 2\mathbf{x}_2 \leq 6\\
& & & -3\mathbf{x}_1 + 2\mathbf{x}_2 \leq 0\\
& & & \mathbf{x}_k \in \mathbb{Z}, & k \in \{1, 2, \dots, |\mathbf{x}|\}\\
\end{aligned}
\end{equation*}
Best Answer
In my opinion, keeping the vector bold is more correct, because you are applying the “extract the $i$-th component” function to the vector.
However, in my experience it is far more common to use the regular font when referring to the components.