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Math Help - symbolic to verbal

  1. #1
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    symbolic to verbal

    I need to write this in verbal form:

    (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))

    I think I'm usually pretty good at this, but all those parentheses are really throwing me off

    This is what I have so far:

    Given any integer x, if x is greater than zero or there is an integer y such that y squared equals x

    Am I on the right track?? Is tehre a simpler form?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by relyt View Post
    I need to write this in verbal form:

    (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))

    I think I'm usually pretty good at this, but all those parentheses are really throwing me off

    This is what I have so far:

    Given any integer x, if x is greater than zero or there is an integer y such that y squared equals x

    Am I on the right track?? Is tehre a simpler form?
    no. saying "if" means you are describing an implication, which is not the case here. you have an expression of the form (\forall x \in A)[P(x) \vee (\exists y \in A)Q(x,y)]

    it is translated as: "for every x \in A, either P(x) or there exists y \in A such that Q(x,y)"
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  3. #3
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    That's pretty cool Jhevon! I'm studying this at the moment, so what you are saying is that there are two propositions of the form P  \vee Q. And the quantifiers remain unchanged?
    I'm not used to using brackets used like this, either. Are these two statements the same:

    x>0) \vee \exists y \in \mathbb{Z}y^2=x) " alt=" \forall x \in \mathbb{Z}x>0) \vee \exists y \in \mathbb{Z}y^2=x) " />

    Or have I missed something with the either ... or?
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  4. #4
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    Quote Originally Posted by relyt View Post
    I need to write this in verbal form:
    (\forall x \in Z) (x > 0 \vee (\exists y \in Z) (y ^{2} = x))
    I would translate this way: Every integer is positive or it is the square of some integer.
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  5. #5
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    Thanks, guys. I think I got it down now. Much appreciated!

    So for the set N of positive integers...this statement: "Every integer is the sum of two other integers".

    would be
    (\forall x \in N+)(x = y + z)

    ??
    Last edited by relyt; March 29th 2009 at 07:49 AM.
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