# What is the meaning of $\bigvee$ (bigvee) operator

What do mean $\bigvee$ operator in page 6 of this document. It is a Variable-sized Math Operator.

What about $\bigwedge$?

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or – anon Jun 28 '12 at 11:29
Is there a point to the self-reference in this post, especially since your title implies that you already know what is the meaning of the symbol... – Asaf Karagila Jun 28 '12 at 11:31
What does this have to do with symbolic computation? – Chris Eagle Jun 28 '12 at 11:35
Might be "minimum". – Djaian Jun 28 '12 at 11:36
This is perhaps "minimum", considering equations 1.5-7 seem to be "translations" of equations 1.2-4 in terms of characteristic functions instead of sets. So $\bigvee \mu_{A_i} = 1$ means the union of the sets is the whole set (equation 1.1). Although I'm not quite sure equations 1.3 and 1.5 are correct: it seems $= \varnothing$ and $=0$ are missing. – Najib Idrissi Jun 28 '12 at 11:40

If you have an indexed family of propositions, say $\{P_\alpha\}_{\alpha \in I}$, then $$\bigvee_{\alpha\in I} P_{\alpha}$$ is the proposition that at least one $P_{\alpha}$ is true. This could also be used for maxima or minima. Another guise might be $$\bigvee_{k=1}^n f_k$$ to express the maximum of $f_1, f_2, \cdots , f_n$.

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"Wedges and vees" ($\wedge,\vee$) are usually used to denote "meets and joins" (respectively) in lattice theory. Roughly speaking "meet" means "greatest lower bound" and "join" means "least upper bound".
As you can see in the document page 6, it looks like they are translating 1.2/1.3/1.4 to 1.5/1.6/1.7. I am very suspicious that there is a typo, because in one spot they have replaced $\cup$ with $\vee$ (and that makes sense, since $\cup$ is a join operator for the lattice of subsets of a set), but they also did the same for $\cap$.
I think possibly they should have replaced $\cap$ with $\wedge$. ($\cap$ is of course, the meet operator in the lattice of subsets of a set.)