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Math Help - Proof that f is injective?

  1. #1
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    Proof that f is injective?

    How would i go about solving this problem?

    Proof that f is injective?-inject.png


    Would i start with f(x) = f(y) ?
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  2. #2
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    Quote Originally Posted by kensington View Post
    How would i go about solving this problem?

    Click image for larger version. 

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    Would i start with f(x) = f(y) ?

    Either I'm missing something or this is immediate: x\neq y\Longrightarrow |f(x)-f(y)|=c|x-y|^\alpha > 0 , and we're done...

    Tonio
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  3. #3
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    Yes, you can start with f(x)= f(y) which, using Tonio's point, immediately gives x= y.
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