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Math Help - Proof

  1. #1
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    Proof

    Prove that x < y, if and only if x + z < y + z

    My work so far:

    Suppose x < y and z >0.
    By definition, y-x and z are an element of the positive numbers (P).


    Then I get lost on how to do the rest of the proof...

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  2. #2
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    Re: Proof

    Quote Originally Posted by AwesomeHedgehog View Post
    Prove that x < y, if and only if x + z < y + z

    My work so far:

    Suppose x < y and z >0.
    By definition, y-x and z are an element of the positive numbers (P).
    If

    Assume $x < y$

    add z to both sides

    $x + z < y+z$

    Only If

    Assume $x+z<y+z$ then

    $x+z-z < y+z-z$

    $x < y$


    QED
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