An acronym used by mathematicians to mean without loss of generality. Usually it is used to mould a part of a proof into a form which is more easily imagined.

For example, in 2D coordinate geometry, a phrase like "Without loss of generality, we can say that the circle is at the origin" is used. Without adding this sentence, every x coordinate in the example (or proof) at hand would have to be replaced with (x - a), and every y coordinate would have to be replaced with (y - b), where (a, b) is the centre of the circle. It is simpler just to do away with a and b, and focus on the core of the issue without any extra distractions. Of course, once the core of the issue is understood, one should go back and check that generality is indeed not lost in translating the origin by (-a, -b). With the understanding of the easier specific case, the extra load of carrying the details of a and b through the proof is reduced dramatically.

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