What exactly does "without loss of generality" mean What exactly does "without loss of generality" mean and how can you formally tell when you are justified in using it? I understand what it means and how to use it informally but is there formal justification for it? When you say "WLOG let a R b" I know that you can't have already said anything about a or b that affects whether a R b. But that doesn't seem very precise. It seems like you need to know that a R b "is not ruled out" by what has been said so far. But is there even a formal way to keep track of what "has been ruled out" and what has not?