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Math Help - simple implication problem

  1. #1
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    simple implication problem

    'x/x-1=0'
    'x=0'
    what is the link between these two statements?
    i would say that its obvious that the link is 'if and only if'!
    but i'm wrong. can someone please help?
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  2. #2
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    Quote Originally Posted by the kopite View Post
    'x/x-1=0'
    'x=0'
    what is the link between these two statements?
    i would say that its obvious that the link is 'if and only if'!
    but i'm wrong. can someone please help?
    Well clearly, \frac{x}{x-1} = 0 \Leftarrow x=0
    Only if x \neq 1, the expression \frac{x}{x-1} is defined and \frac{x}{x-1} = 0 \Rightarrow x=0
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  3. #3
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    Hello, the kopite!

    \begin{array}{c}\dfrac{x}{x}-1\:=\:0 \\ \\[-4mm]  x\:=\:0 \end{array}

    What is the link between these two statements?

    Not sure how to describe a "link" . . .

    The two statements are mutually exclusive.
    . . Only one of them can be true.


    If \frac{x}{x}-1 \:=\:0, then: . \frac{x}{x} \:=\:1 . . . which is true if x \neq 0


    If x = 0, the other statement is not true because \frac{0}{0} is indeterminate.

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  4. #4
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    soroban got my question wrong, sorry if i didnt explain my equation properly. but i didnt understand the second part of ismorphism's explanation. i'm slow on genral reasoning.
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  5. #5
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    Quote Originally Posted by the kopite View Post
    'x/x-1=0'
    'x=0'
    what is the link between these two statements?
    i would say that its obvious that the link is 'if and only if'!
    but i'm wrong. can someone please help?
    I agree that it is 'if and only if'.

    If x=0 then \frac{x}{x-1}=0. If \frac{x}{x-1}=0 then x=0.

    Both of those are true statements.
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