While writing a paper, I recently started having a doubt when it comes to write mathematical equations that have to be referenced later as "Equ. (1)" and similar. The issue is if it is better or not to include in the equation the domain over which the variables range. An explanatory example:
First version:"We have proved that
$(1) \qquad f(n) = f(n - 1)^2 + 1$
for every integer $n \geq 2$."
Second version:"We have proved that
$(1) \qquad f(n) = f(n - 1)^2 + 1 \quad (n \geq 2) .$"
I always thought that the first version was fine, but now I wonder if instead it is slightly improper because a sentence like "From (1) it follows that..." does only refer to $f(n) = f(n - 1)^2 + 1$ without specifying the range of $n$.
The second version solves this problem, but the statements "for every integer $n \ge 2$" has to be shortened to $(n \geq 2)$ for space reasons. Also, the second version might look ugly if the equation number has to be put on the right:
$f(n) = f(n - 1)^2 + 1 \quad (n \geq 2). \quad (1)$
Are there any recommendations about the two versions? I could not find anything in mathematical writing guidelines.