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## What is the best notation for this set?

I have variables that are indexed by $x$ and $y$: $V_{xy}$. What is the best notation for "all $V_{x1}$ variables, for $x=1,\dots,X$"?

I'd like to write something like "I set all variables $\{V_{x1}, x=1,\dots,X\}$ to zero."

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What's wrong with something like: Set $V_{x1}=0$ for all $1 \leq x \leq X$. – Douglas S. Stones Jan 31 2010 at 4:23
Seconding Douglas' comment: there's nothing wrong with what you've written, and I can't think of any real improvement – Yemon Choi Jan 31 2010 at 4:38

Set the variables $V_{11}, V_{21}, \ldots, V_{X1}$ equal to zero.
Morse-Kelley class theory would allow such a class: $\{z:\exists(x,y)(z=V_{xy};x\in\{1,\ldots,X\};y=1)\}$; in Zermelo-Fraenkel set theory you should also specify from which set $Z$ you choose $z$: this of course depends on what you mean by $V_{xy}$.