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Math Help - Simple problem. Did I get it right?

  1. #1
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    Simple problem. Did I get it right?

    If a|b and b|a, is a=b?

    I did as follows: If a|b, there is a number r in \mathbb{Z} such that b=r\cdot a.
    Likewise, if b|a, there is a number s in \mathbb{Z} such that a=s\cdot b.

    This shows us that a=r\cdot s \cdot b and b=r\cdot s \cdot a. Because of this, r=s^{-1}.
    r and s er both in \mathbb{Z}, therefore r=s=1 and \underline{\underline{a=b}}

    Was my reasoning here correct, and did I get the right answer?
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  2. #2
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    No, a = |b|.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    No, a = |b|.
    No, |a| = |b|
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