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What does this symbol mean?

  1. Aug 26, 2012 #1
    I would like to know what this symbol means:[tex]\nVdash[/tex]Specifically, in the main result of [link] (Theorem 1, at the top of p.4), it has:[tex]\nVdash(n=k=0)[/tex]
     
  2. jcsd
  3. Aug 26, 2012 #2
    It is negation of [tex]\Vdash[/tex] and the latter means "entails".
     
  4. Aug 26, 2012 #3
    Yes, I saw the [itex]\Vdash[/itex] symbol listed as "entails" in Wikipedia's list of mathematical symbols. However, in that article, the explanation is "A [itex]\Vdash[/itex] B means the sentence A entails the sentence B, that is in every model in which A is true, B is also true."

    I can't see how that applies to my example (which is not in the form[itex]A \nVdash B[/itex]).
     
  5. Aug 26, 2012 #4

    Bacle2

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    Science Advisor

    How about : the cases described are excluded, i.e., the definition excludes the

    cases n=k=0 ?
     
  6. Aug 26, 2012 #5
    This still does not seem to make sense in the given context. The relevant phrase in full is:[tex]\mathrm{where \ } R_{n,0,k}(x) \ := \ \nVdash(n=k=0), \ \ R_{n,j,0} \ := \ \nVdash(n=j) \mathrm{ \ \ and \ \ } R_{n,j,k} \ := \ 0 \ \mathrm{else}[/tex]
     
  7. Aug 27, 2012 #6
    I've spent a long time trying to reverse engineer the phrase. My best guess is that the whole phrase (see previous post) could translate into the following two statements:

    [tex]R_{n,0,k}=\left\{
    \begin{array}{c}
    1, \\
    0,
    \end{array}
    \begin{array}{l}
    \text{if }n=k=0 \\
    \text{otherwise}
    \end{array}
    \right. [/tex]
    [tex]R_{n,j,0}=\left\{
    \begin{array}{c}
    1, \\
    0,
    \end{array}
    \begin{array}{l}
    \text{if }n=j \\
    \text{otherwise}
    \end{array}
    \right.[/tex]
    Even if this is correct, there are other bits of notation that I don't understand... but I suppose I should start a new thread, as this one seems pretty dead.
     
  8. Aug 27, 2012 #7
    Why don't you get in touch with the author of the article?
     
  9. Aug 27, 2012 #8

    micromass

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    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Good idea. It looks like a typo. So you should ask the author.
     
  10. Aug 27, 2012 #9
    Yeah, I've E-mailed the author... fingers crossed that I get a reply, I suppose.
     
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