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Math Help - A Quick Question on Valid Set Builder Notation

  1. #1
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    A Quick Question on Valid Set Builder Notation

    Hello; today my Precalculus teacher gave this definition for the set of rational numbers:
    Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}
    Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
    Shouldn't it be:
    Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}
    or
    Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}?
    Thanks,
    yottaflop
    Last edited by yottaflop; July 5th 2011 at 01:13 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: A Quick Question on Valid Set Builder Notation

    Quote Originally Posted by yottaflop View Post
    Hello; today my Precalculus teacher gave this definition for the set of real numbers:
    Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}
    Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
    Shouldn't it be:
    Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}
    or
    Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}?
    Thanks,
    yottaflop

    Your Precalculus teacher is wrong!

    \mathbb{Q} is set of all rational numbers.

    Here you can find some information:

    Real number - Wikipedia, the free encyclopedia


    Rational number - Wikipedia, the free encyclopedia
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  3. #3
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    Re: A Quick Question on Valid Set Builder Notation

    Hello, yottaflop!

    A few spaces will provode clarity.

    . . Q \:=\: \{ r\,|\,r= \tfrac{a}{b},\;a,b \in Z,\;b \ne 0 \}


    I seriously doubt that a textbook would write it like this:

    . . Q\!=\!\{r|r\!=\!\tfrac{a}{b},\!a,\!b\!\in\!Z,\!b\!  \ne\!0\}


    If it does, it may bring back public flogging.

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  4. #4
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    Re: A Quick Question on Valid Set Builder Notation

    Thank you both; Also sprach: that was a typo on my part, sorry for the confusion. I've edited my original post to fix it.
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  5. #5
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    Re: A Quick Question on Valid Set Builder Notation

    Quote Originally Posted by Soroban View Post
    Hello, yottaflop!

    A few spaces will provode clarity.

    . . Q \:=\: \{ r\,|\,r= \tfrac{a}{b},\;a,b \in Z,\;b \ne 0 \}


    I seriously doubt that a textbook would write it like this:

    . . Q\!=\!\{r|r\!=\!\tfrac{a}{b},\!a,\!b\!\in\!Z,\!b\!  \ne\!0\}


    If it does, it may bring back public flogging.

    I will direct you to this scrappy pack of textbook editors that have decided monkeys para-shooting out of planes and tightrope walking clowns will 'help' explain the math...
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  6. #6
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    Re: A Quick Question on Valid Set Builder Notation

    Quote Originally Posted by yottaflop View Post
    Hello; today my Precalculus teacher gave this definition for the set of rational numbers:
    Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}
    =Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
    Shouldn't it be:
    Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}
    or
    Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}?
    Thanks,
    yottaflop
    The second is better than what you initially give. The first of your suggestions is definitely wrong since it is requiring that the set, {a, b}, be an integer!
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