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Thread: Simple problem. Did I get it right?

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

    If $\displaystyle a|b$ and $\displaystyle b|a$, is $\displaystyle a=b$?

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

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

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