A phrase popular in mathematics, when doing a proof. It means you're looking at essentially a specific case, but that case is trivially equivalent to all the cases out there. So you might say "...and now we pick an element from the list. Without loss of generality, let it be the first element." You can do this, because, at least in the context of the proof at hand, it doesn't really matter which element you picked, and if it wasn't the first one, well, just renumber them so it is. It just makes your notation easier as you go along. Also used with arguments by symmetry: show something is true for one of several nearly-identical parts of the problem (the top half, or the even cases, or something like that), so that it's trivial to see how it applies to the rest of the situation. That subcase is presented without loss of generality (or the rest are said to follow by symmetry).

Often abbreviated "wlog" in proofs.

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