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Thread: Need help on working through this proof.

  1. #1
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    Need help on working through this proof.

    Am I doing the right approach as to why I reasoned it is not necessary or am I completely off? This is 3.7 on my paper. Not 3.6.

    https://imgur.com/Xmibmbl

    Also skipped some algebra steps, but am sure everyone here can comprehend xD. thank you for help!
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  2. #2
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    Re: Need help on working through this proof.

    Quote Originally Posted by math951 View Post
    Am I doing the right approach as to why I reasoned it is not necessary or am I completely off? This is 3.7 on my paper. Not 3.6.

    https://imgur.com/Xmibmbl

    Also skipped some algebra steps, but am sure everyone here can comprehend xD. thank you for help!
    Please state which of the two you are asking about?
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  3. #3
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    Re: Need help on working through this proof.

    The 2nd problem (3.7). But if you want you can tell me what you think of 3.6 as well. Do you see it as very formal?
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    Re: Need help on working through this proof.

    Quote Originally Posted by math951 View Post
    The 2nd problem (3.7). But if you want you can tell me what you think of 3.6 as well. Do you see it as very formal?
    If $a\ne b$ then $|a-b|>=0$ therefore we have:
    $\begin{align*}(a-b)^2&>0 \\a^2-2ab+b^2&>0\\a^2+2ab+b^2&>4ab\\(a+b)^2&>4ab \end{align*}$

    Now suppose that $(a+b)^2>4ab$
    $\begin{align*}(a+b)^2&>4ab \\a^2+2ab+b^2&>0\\a^2+2ab+b^2&>4ab\\a^2-2ab+b^2&>0\\(a-b)^2&>0 \end{align*}$

    That implies that $a\ne b$.
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  5. #5
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    Re: Need help on working through this proof.

    Thanks. I'll check this proof out after I finish chapter 4 (contradiction) and chapter 5 (induction).

    For contradiction, in essence we have a proof, and then we have a statement P. We then basically suppose a contradiction and say not P, and if not P is false. Then that is contradiction and implies original statement is correct?
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