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A Lipschitz Proof

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  1. Jul 6, 2016 #1
    I was reading this book yesterday and looking at this proof/justification. I was thinking it is possibly incorrect, but wanted to get some other opinions. Here is the example they gave in the book with the work attached.

    upload_2016-7-6_8-50-23.png

    upload_2016-7-6_8-50-53.png
     
  2. jcsd
  3. Jul 6, 2016 #2

    fresh_42

    Staff: Mentor

    Looks ok to me. What does make you think it might be incorrect?
     
  4. Jul 6, 2016 #3
    I guess what threw me off was the ending. I was just expecting to see something stating therefore the the function is Lipschitz. I guess in the book, they wanted you to just in your head think that.
     
  5. Jul 6, 2016 #4

    fresh_42

    Staff: Mentor

    Well, it's the definition of Lipschitz continuity. If one has to show a number ##n## is even and shows it is divisible by ##2##, nobody would complain about a missing "... therefore ##n## is even", because we are used to the concept of even numbers. It is the same here: simply a matter of acquaintance. Maybe it would be a little more obvious if one had chosen ##L## instead of ##M## as the constant.
     
  6. Jul 6, 2016 #5
    Yeah I see what you are saying now. It makes sense. Thanks.
     
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