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Math Help - range of x-y

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    range of x-y

    What is the range of "x-y is a rational number"? Where x and y are set of real numbers.

    is it -- (0,0), (1/2,-1/2), (1/3, 4/3)?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by robocop_911 View Post
    What is the range of "x-y is a rational number"? Where x and y are set of real numbers.

    is it -- (0,0), (1/2,-1/2), (1/3, 4/3)?
    Your question is confusing. A function f:A \to B maps the members of the set A to members of the set B. The set A is called the domain and B is called the range. (To put it in simple terms anyway.) To define an expression "x - y" is a rational number where x and y are the set of real numbers makes little sense to me.

    Now, if you are merely asking what is the size of the set \{ x - y \in \mathbb{Q}|x, y \in \mathbb{R} \} (i.e. The set of all real numbers x and y such that x - y is rational) then your answer is that the size of your set is infinite. Given any value of x we can find an infinite number of y values such that x - y is rational.

    I think this addresses your question. If not, just let me know.

    -Dan
    Last edited by topsquark; June 7th 2008 at 06:04 PM.
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    Quote Originally Posted by topsquark View Post
    Your question is confusing. A function f:A \to B maps the members of the set A to members of the set B. The set A is called the domain and B is called the range. (To put it in simple terms anyway.) To define an expression "x - y" is a rational number where x and y are the set of real numbers makes little sense to me.

    Now, if you are merely asking what is the size of the set \{ x - y \in \mathbb{Q}|x, y \in \mathbb{R} \} (i.e. The set of all real numbers x and y such that x - y is rational) then your answer is that the size of your set is infinite. Given any value of x we can find an infinite number of y values such that x - y is rational.

    I think this addresses your question. If not, just let me know.

    -Dan
    My mistake its not "Range" it is the topic of "Relations" - I just have to find the pair of elements given the "condition of the relation" i.e. x-y is a rational no., So I am wondering what the pair of elements might be...
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    You have a relation R such that \left( {x,y} \right) \in R \Leftrightarrow \,\left( {x - y} \right) \in Q.
    The range of any relation is the set of second terms.
    What is the set of all second terms in R? How is a difference of two reals rational?

    Here are examples.
    \left( {2,\frac{1}{2}} \right) \in R because \left( {2 - \frac{1}{2}} \right) is rational.
    \left( {\pi ,\pi } \right) \in R because \pi  - \pi  = 0 and zero is rational.
    Does that mean that R is reflexive?
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