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Thread: Product Sets Help

  1. #1
    Newbie
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    Aug 2009
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    Product Sets Help

    Hi everyone,

    I was wondering if someone felt inclined to give me a hand understanding a question that I'm stuck on? It's really bugging me because I think I'm missing something quite simple here!

    The question is:

    For each of the following subsets of $\displaystyle \mathbb{R} \times \mathbb{R}$, determine whether it can be written as a product of two subsets of $\displaystyle \mathbb{R}$. If it can, what are these subsets?

    (i) $\displaystyle A_{1} = {(x,y) : 0 \leq y < 1}$
    (ii) $\displaystyle A_{2} = {(x,y) : x^2 + y^2 < 3}$
    (iii) $\displaystyle A_{3} = {(x,y) : x<y}$
    (iv) $\displaystyle A_{4} = {(x,y) : x \mbox{ is an integer, and }y \mbox{ is not an integer}}$

    As I said, I'm sure I'm missing something fairly simple but I'm really not sure what it is!

    Thanks a lot in advance!
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  2. #2
    MHF Contributor
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    Here is the first one to help you
    (i) $\displaystyle A_{1} = {(x,y) : 0 \leq y < 1} = \mathbb{R} \times [0,1[$
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