What's the best math form of ‘point set' in an article?

Question

I am writing a short article on clustering. Suppose each element of a group of $N$ points is denoted as $\mathbf{x}_i$, Which of the following is proper to denote this point set?

1. $\mathbf{X}=\{\mathbf{x}_i, i = 1, \cdots, N\}$ or
2. $X=\{\mathbf{x}_i, i = 1, \cdots, N\}$

Thanks a lot.

Answer 1

My preference would be $X = \{\mathbf x_1, \ldots, \mathbf x_N\}$.

In many cases in mathematics, symbols don’t have any fixed meaning, so you are free to call things whatever you want. In cases where there are customary symbols, you should use them, to make your work easier to understand. But if you go against the conventions, that doesn’t make your work wrong, it just makes it unusual and hard to read.