What is the correct way of writing a vector element? 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*}
 A: 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.
A: I prefer the first. I think of starting with an indexed set of scalars $\{x_i\}$ (not bold, italicized, as normal) for $i \in \{1,\ldots,n\}$. Then from those scalars I build $\mathrm{\mathbf{x}}=[x_1,\ldots,x_n]^{\top}$, an object with a different data type (vector) which uses math roman and bold to indicate its different type. 
A: I personally prefer the first method, without boldface.The reason is that the from first glance, it is clear that you are adding scalars. The second way seems like you are doing vector operations from first glance.
What matters is consisenty, I like to use normal face for elements  ($x_i$ is $i$th element of $x$) and boldface for counters (e.g. $\mathbf{x}_i$ is the $i$th vector of type $\mathbf{x}$). But this becomes a problem when you use a counter and index at the same time, i.e. should it be

*

*$x_{i,j}$ is the $j$th element of the $i$th vector $\mathbf{x}$

*or $\mathbf{x}_{i,j}$ is the $j$th element of the $i$th vector $\mathbf{x}$?

Hence the problem resurfaces, and in this case I would go for option two!
