Proper notation for enumeration

Question

Between these two options, is there a best practice notation for enumeration or are they both equivalently acceptable: \begin{equation} \forall i = 0,1,\dots,n-1 \qquad (1) \end{equation} \begin{equation} \forall i \in \{0,1,\dots,n-1\} \qquad (2) \end{equation}

Thank you for your answers.

NS

Answer 1

Both notations see widespread use in the literature. The second version has the downside of being slightly more cumbersome to write down (and to typeset using $\LaTeX$) but it offers the advantage of being more versatile (in that it carries over to any, potentially infinite, index set) and, arguably, more formal.

In the end, I don't see a striking advantage of either notation and I don't think anyone would be confused even if you mixed and matched it at will.

Answer 2

In my personal opinion, both are OK, but the $\forall$ sign is reduntant. I'd rather write

"for $i=0,\dots,n$".