- #1

Kostas Tzim

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- Thread starter Kostas Tzim
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- #1

Kostas Tzim

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- #2

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Context ? Assume WHAT?

- #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:

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.

- #4

Kostas Tzim

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i understand thanks!

- #5

HallsofIvy

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Sometimes abbreviated "wlog".

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