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Does anybody know a commonly used symbol for WLOG (without loss of generality)? I'm not comfortable with typing the whole thing every time and the abbreviation is just a compromise. If there is one for QED, why shouldn't there be one for WLOG? :)

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Find what WLOG is in latin, and then abbreviate it? Maybe? If google traduction is right, it would be absque amissione generalitate which would become AAG... –  Jean-Sébastien Oct 22 '12 at 15:03
What’s wrong with WLOG? (Well, okay, if you write in German you should probably prefer o.B.d.A. or o.E.d.A, ohne Beschränkung/Einschränkung der Allgemeinheit. :-)) –  Brian M. Scott Oct 22 '12 at 15:05
I don't understand the downvote on this one. It is a perfect fine question with a clear answer. –  Thomas Oct 22 '12 at 15:14
You could try $\log_w$. But seriously, I dislike the use of WLOG (or what it stands for) as a somewhat careless way of writing, that puts an additional burden on the reader (because there is loss of something, namely freedom; for instance if you've used some symmetry to justify the WLOG, you can't use the same kind of reduction again) and if you are using it all the time, you might want to adopt a different style. –  Marc van Leeuwen Oct 22 '12 at 15:38
@Marc: It can be certainly misused, but eschewing it entirely puts a different additional burden on the reader: unnecessary clutter. –  Brian M. Scott Oct 22 '12 at 15:54

3 Answers 3

up vote 8 down vote accepted

To answer your question: No there is no commonly used symbol for WLOG.

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On the contrary, WLOG is a perfectly common symbol for WLOG ;) –  Arkamis Oct 22 '12 at 15:26
@Ed: With WOLOG stumbling woefully along behind it. :-) –  Brian M. Scott Oct 22 '12 at 15:28
All right, I guess I'll create my own symbol for that. –  Count Zero Oct 22 '12 at 16:02
Perhaps SLOG, for sans loss of generality –  Arkamis Oct 22 '12 at 16:21
@EdGorcenski: or KG for keeping generality. –  Thomas Oct 22 '12 at 17:07

In German, the equivalent phrases "ohne Beschränkung der Allgemeinheit" (oBdA) or "ohne Einschränkung" is sometimes denoted by Œ (O-E ligature):

Π$ a<b \Rightarrow \ldots$

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Since there doesn't seem to be any such symbol, I decided to create one, by manipulating $\forall$ and $\exists$. Any thoughts?

enter image description here

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No thoughts, only downvotes. Of course, if any site were going to introduce new math notation, shouldn't it be this one? –  The Chaz 2.0 Oct 22 '12 at 18:03
@TheChaz: I don't think that this site should attempt and try to introduce notational conventions. I also don't think that WLOG should have a symbol. I think that if you're still at the stage where you try to write a proof only by mathematical symbols then you are not ready to use WLOG in your proofs. (I didn't vote on this answer, by the way, neither up nor down). –  Asaf Karagila Oct 22 '12 at 18:06
I don't think that WLOG needs a new symbol, because I find that the phrase "without loss of generality" is almost always used in written text, not symbolic notation. The phrase itself means, more or less, that one may restrict one's attention to a specific (usually simpler) case without losing completeness or rigor in the presentation. If used symbolically, it is not necessarily clear that this is true. WLOG is also a dangerous phrase; its use can be as haphazard and incorrect as "clearly" and "obviously". –  Arkamis Oct 22 '12 at 18:15
What if you describe protocols or algorithms? I've seen several cases where WLOG is mixed with other math notation. I prefer to have either only symbols or things spelled out. Spiking it with SFLAs is not to my liking. Because I prefer to keep such things concise, I'd rather have a new symbol than WLOG. –  Count Zero Oct 22 '12 at 18:24
@TheChaz: Thanks for 'No thoughts, only downvotes'. –  Count Zero Oct 22 '12 at 18:26

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