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Does the term "without restriction of generality" mean the same as "without loss of generality"?

EDIT: I encountered the phrase in this paper (PDF).

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in what context did you encounter it? – Holdsworth88 Aug 15 '12 at 10:15
Yes. It has the distinct smell of a Germanism. It's the literal translation of Ohne Beschränkung der Allgemeinheit or Ohne Einschränkung der Allgemeinheit which mean exactly the same as WLOG. In lectures and informal notes the abbreviations OBdA and OE are very common. It's hard to be entirely sure without context or source, though. – t.b. Aug 15 '12 at 10:20
@Holdsworth88: in a paper on triangulation, it says without restriction of generality, let $(p_1^{1},p_1^{2})$ denote an initial edge of triangulation... – PeteUK Aug 15 '12 at 10:24
@t.b.: The primary author is Petra Wiederhold which sounds Germanic to me. – PeteUK Aug 15 '12 at 10:26
up vote 9 down vote accepted

Yes, it means exactly the same as without loss of generality (in the linked paper the authors assume that $(p_1^{(1)},p_1^{(2)})$ is an initial segment of the triangulation, not just any segment).

The formulation has the smell of a Germanism to me — which is confirmed by the fact that one of the authors of the paper is of German origin as her CV reveals.

Without restriction of generality is a literal translation of ohne Beschränkung der Allgemeinheit or ohne Einschränkung der Allgemeinheit which both mean exactly the same as WLOG. In lectures and informal notes the abbreviations o.B.d.A., o.E.d.A. or simply o.E. (or the symbol Œ) are very common in German speaking countries.

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Actually, one usually uses a lower case o unless at the beginning of a sentence (because German is "case sensitive", and the o is for "ohne", which is written in lowercase), and uses dots (also a general rule of German abbreviations): "o.B.d.A." – celtschk Aug 15 '12 at 10:52
Is this better? Thanks, being almost an elderly guy, I've forgotten all the orthography rules (I know I shouldn't have). It's been a while since I last needed to write in German... – t.b. Aug 15 '12 at 10:57
I figured it might mean the initial segment doesn't have to be the segment with endpoints from the first point from each contour but for the purposes of their subsequent explanation, they'll assume it is. – PeteUK Aug 15 '12 at 11:00
I'm not sure if the dots would be set for "OE"/"O.E." (that one doesn't follow the German abbreviation rules anyway, and I've never seen it before, so I don't know how it is usually written), however the dots with "o.B.d.A" and "o.E.d.A." are right now, as is the lower-case "ohne" in the spelled-out version. – celtschk Aug 15 '12 at 11:06

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