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Suppose there are several cases which need to be investigated.

If the same argument can be used to dispose of two or more of these cases, then it is acceptable in a proof to pick just one of these cases, and announce this fact with the words: Without loss of generality, ..., or just WLOG.

When communicating mathematics verbally, it is becoming commonplace to use the vocalisation wullog rather than the timewastingly multisyllabic without loss of generality.