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Without any loss of generality

  1. Aug 19, 2015 #1
    Hello guys can someone please explain to me how to use the assertion, "without any loss of generality assume...", i find it kind of tricky to use...a simple example would be useful too. :)
     
  2. jcsd
  3. Aug 19, 2015 #2

    phinds

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    Context ? Assume WHAT?
     
  4. Aug 19, 2015 #3

    jbriggs444

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    Tossing out an example: If a and b are distinct real numbers prove that a^2 + b^2 > 2ab.

    Proof:

    Without loss of generality, assume a > b [... rest of proof ensues ...]

    We can make this assumption because a and b are distinct. Either a > b or b > a. If a > b then our assumption is true. If b > a then we could reverse the labels and the re-labelled assumption is true. The rest of the proof would go through either way. There is no point in writing essentially the same proof twice, once with labels a and b and then again with labels b and a.

    The "without loss of generality" phrasing is used to indicate that this sort of situation exists -- that all of the cases under consideration are really just re-labellings of a single base case and that no other possibilities exist.
     
  5. Aug 20, 2015 #4
    i understand thanks!
     
  6. Aug 20, 2015 #5

    HallsofIvy

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    Sometimes abbreviated "wlog".
     
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