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Math Help - for all quantifier

  1. #1
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    for all quantifier

    Hello

    A is a formula with variables x and y. What is the difference between

    \forall (x,y) A

    \forall (x) \forall (y)A

    Thank you...
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  2. #2
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    Re: for all quantifier

    Unless there's some special context in mind, I'd take them both as the same.

    [Here using 'A' for the quantifier in ASCII:]

    AxAyP

    AxyP

    some people write

    (x)(y)P

    They all mean the same.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: for all quantifier

    What makes you think that there is a difference?
    Can you come up with any examples where they wouldn't be the same?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: for all quantifier

    If \mathcal{L} is a first order language with variable letters x,y,\ldots then, (\forall x)(\forall y)A is a well formed formula and (\forall (x,y))A it is not. We can of course use (\forall (x,y))A as an alternative notation for (\forall x)(\forall y)A .
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  5. #5
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    Re: for all quantifier

    I'd rather avoid the clutter of parenethess. It's enough to have

    AxAyP

    And then to allow that to be indicated by

    AxyP
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  6. #6
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    Re: for all quantifier

    Thank you all for your replies .
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