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Is there a conventional notation for the set of all vectors of length $n$ such that not one element of the vector is equal to zero?

Right now I have to write out something like "vector $B$ blah blah blah, where

$B \not\in \left\{A =[a_1, a_2, a_3, ..., a_n], \textrm{ where } \forall i, a_i \neq 0 \right\}$.

I'm wondering if there is a more compact/conventional way to express this?

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I don't know of any widely spread convention for that. If you like you might write $\Pi_1^n a_i \not= 0$, dunno if you find it any nicer than what you wrote – mm-aops Jul 29 '14 at 16:29
$(a_1,..,a_n)\in(K^\times)^n$ where $K$ is the coefficient field, is another possibility. – Andrea Mori Jul 29 '14 at 17:02
How about $(a_i)_{i = 1}^n \in (K^\times)^n$? – Ivo Terek Jul 29 '14 at 18:04
What are the coordinates good for? Why not just $A ≠ 0$? – user87690 Jul 30 '14 at 15:13

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