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Thread: Product Sets Help

  1. #1
    Aug 2009

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

    (i) A_{1} = {(x,y) : 0 \leq y < 1}
    (ii) A_{2} = {(x,y) : x^2 + y^2 < 3}
    (iii) A_{3} = {(x,y) : x<y}
    (iv) 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
    Nov 2008
    Here is the first one to help you
    (i) A_{1} = {(x,y) : 0 \leq y < 1} = \mathbb{R} \times [0,1[
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