I want to write "$x,y > 0$".

Question

I want to write "$x,y > 0$". Can I do this? Or do I have to write "$x > 0$ and $y > 0$"? Which one is the proper way to write in maths?

Answer 1

It's commonly used notation, so yes. And even if it wasn't, you can always define notation in the beginning, and then use it. In this case, you'd see something like "For brevity, we will use $x,y,\ldots>0$ to mean $x>0$, $y>0$, etc. in the rest of the article."

Answer 2

I always do that, however be careful if you want to write $a < x < b$ and $a < y < b$, since $a < x,y < b$ is ambiguous. One would have to write $x,y \in (a,b)$.

Answer 3

Yes, you can do that. Either way is fine, but, of course, the former is more concise.

Answer 4

Its fine if it dont lead to some ambiguity. An alternative notation can be $x,y\in\Bbb R_{>0}$. Or just $x,y\in[0,\infty)$.