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  1. #1
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    Favourite logical operator

    This used to be my favourite operator. It can do everything the other operators do. Just an example of what it does.

    ~(p&~p) :: p|(p|p)

    p&~p :: (p|(p|p))|(p|(p|p))

    ~(p&~p)&(p&~p) :: ((p|(p|p))|((p|(p|p))|(p|(p|p))))|((p|(p|p))|((p|( p|p))|(p|(p|p))))

    I was going to add a poll, but after doing that translation, I can't be bothered.

  2. #2
    CC Grandmaster Basil's Avatar
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    What does it mean? What could one use it for?
    There is no cure for leftism. Its infestation of the host mostly diminishes with age except in the most rabid of specimens.

  3. #3
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    Quote Originally Posted by Gunner Duggan
    What does it mean?
    English translation of it would be "not both".
    Quote Originally Posted by Gunner Duggan
    What could one use it for?
    Aside from amusing logic students, there is the NAND gate. The NAND gate functioning the same way. Easy to make. Since NAND can do all, you can make your computer chips with just NAND gates. (Roughly anyway, I am not a computer expert.)

  4. #4
    CC Grandmaster Basil's Avatar
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    And I thought English was difficult!
    There is no cure for leftism. Its infestation of the host mostly diminishes with age except in the most rabid of specimens.

  5. #5
    Reader in Slood Dynamics Rincewind's Avatar
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    Quote Originally Posted by Mangafranga
    ~(p&~p) :: p|(p|p)
    AFAICT the shortest way to write 1 with just an indeterminate p and the stroke (and parentheses).

    Quote Originally Posted by Mangafranga
    p&~p :: (p|(p|p))|(p|(p|p))
    AFAICT the shortest way to write 0 with the same restrictions.

    Quote Originally Posted by Mangafranga
    ~(p&~p)&(p&~p) :: ((p|(p|p))|((p|(p|p))|(p|(p|p))))|((p|(p|p))|((p|( p|p))|(p|(p|p))))
    A long winded way to write 0.

    Quote Originally Posted by Mangafranga
    I was going to add a poll, but after doing that translation, I can't be bothered.
    You're not fooling anyone. I vote for the upside down A, universal quantification symbol, even though we aren't talking predicate logic, just to be difficult. Although as a relativist (as opposed to an absolutist) perhaps the upside down E is more my style.
    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  6. #6
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    Quote Originally Posted by Rincewind
    A long winded way to write 0.
    Indeed the fact that it is truth functional kind of kills the fun a bit. Let us call it a Zcheffer stroke. It translates from one of the logic's where the second two formulae are not equivalent. Or maybe even simpler- it translates from English! (But then I have to define "~" as "not" and so on, but this should be simple.)
    Quote Originally Posted by Rincewind
    You're not fooling anyone. I vote for the upside down A, universal quantification symbol, even though we aren't talking predicate logic, just to be difficult.
    I didn't mean to restrict things to predicate, first order or anything else. I regretted adding "it can do everything the other operators can do", as it can only do so within a limited context.
    Quote Originally Posted by Rincewind
    Although as a relativist (as opposed to an absolutist) perhaps the upside down E is more my style.
    As long as you don't cheat and say things like ~E(x)~(Fx->Gx).

    I do find quantification quite beautiful in general. Confused A more so than confused E.
    Last edited by Aaron Guthrie; 07-04-2008 at 12:38 AM.

  7. #7
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    After a bit of thought I have decided my current favourite is... negation! But especially non-Boolean negation!

    N.B. I am going to be spending the next couple of months writing an essay on such. So look forward to me disowning that as a favourite

    P.S. N.B. I will be in a quandry on how to disown it (that one symbol will not be welcome).

  8. #8
    CC Grandmaster Spiny Norman's Avatar
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    I recall reading about NAND gates when I did an IT course about 10 years ago. Forgotten it all now unfortunately, but we had to use them to design circuits.

    As for !negation ... I'm a positive sort of chap, so I couldn't pick that.

    EDIT: ficksed speling tiepo
    Last edited by Spiny Norman; 07-04-2008 at 01:57 PM.
    “As you perhaps know, I haven't always been a Christian. I didn't go to religion to make me happy. I always knew a bottle of port would do that. If you want a religion to make you feel really comfortable, I certainly don't recommend Christianity.” -- C.S.Lewis

  9. #9
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    Quote Originally Posted by Spiny Norman
    As for !negation ... I'm a positive sort of chap, so I couldn't pick that.
    But you surely did use it in not picking it! Another Russell fact- he tried to eliminate negation.

    (Also just a note on my previous post- that essay isn't for a logic subject, it is an Aristotle subject. Essay is really on his argument against contradiction, and Boolean negation is an important issue in such.)

  10. #10
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    This post reminded me of another cool operator (if I could do induction I might conclude that all operators are cool). The relevant arrow! This means whenever anyone writes "->" you can say, "Is that a relevant arrow?". Trust me, it is great fun.

  11. #11
    Reader in Slood Dynamics Rincewind's Avatar
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    So einfach wie möglich, aber nicht einfacher - Albert Einstein

  12. #12
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