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Universal quantifiers, foundations and logic Watch

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    The statement

    "For every prime x there is a larger prime y"

    which translates to (P is the set of primes)

    \forall x \in \mathbb P\ \exists\ y \in \mathbb P\ s.t\ y>x

    I'm proposing that you can switch y>x and y \in \mathbb P and that this version is the same as the one up above.

    However my teacher said that this is incorrect why so?
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    (Original post by will'o'wisp2)
    The statement

    "For every prime x there is a larger prime y"

    which translates to (P is the set of primes)

    \forall x \in \mathbb P\ \exists\ y \in \mathbb P\ s.t\ y>x

    I'm proposing that you can switch y>x and y \in \mathbb P and that this version is the same as the one up above.

    However my teacher said that this is incorrect why so?
    The scope of the quantifier follows the quantifier. It's part of the logical sentence syntax.

    If you make the change you suggest the y in y>x will not be constrained by the existential quantifier, and the quantifier would be left hanging at the end. Just doesn't make sense.
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    (Original post by ghostwalker)
    The scope of the quantifier follows the quantifier. It's part of the logical sentence syntax.

    If you make the change you suggest the y in y>x will not be constrained by the existential quantifier, and the quantifier would be left hanging at the end. Just doesn't make sense.
    took me a long time but i understand i think, so you read it like a sentence from left to right and it makes no sense if you state what y is before you define what it is right?
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    (Original post by will'o'wisp2)
    took me a long time but i understand i think, so you read it like a sentence from left to right
    Yes.

    and it makes no sense if you state what y is before you define what it is right?
    I think it best to say, if you're intending to define a variable, you must do so before you use it. And leave it at that.
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    (Original post by ghostwalker)
    Yes.



    I think it best to say, if you're intending to define a variable, you must do so before you use it. And leave it at that.
    ye just what i meant(maybe not what i said xD) thanks man
 
 
 
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