9
$\begingroup$

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

What about $\bigwedge$?

  • 1
    [or](http://en.wikipedia.org/wiki/Logical_disjunction)2012-06-28
  • 2
    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...2012-06-28
  • 0
    What does this have to do with symbolic computation?2012-06-28
  • 1
    Might be "minimum".2012-06-28
  • 0
    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.2012-06-28
  • 0
    Thanks. I withdraw my vote to close, and I undid my downvote.2012-06-28

2 Answers 2

9

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 $f_1, f_2, \cdots , f_n$.

  • 0
    Can you please suggest a link for more information?2012-06-28
  • 0
    Here is one place you will see it used a little: http://en.wikipedia.org/wiki/Lattice_(order)2012-06-28
  • 0
    It seems the above usage (your answer) is different from mentioned wiki link, is not it?2012-06-28
4

"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".

This will come up in logic too because logical conditionals have interpretations as"meets and joins".

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.)