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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? :)

Count Zero
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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
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    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 didn't ask for translation, I just want to know whether there is a symbol for WLOG. What's wrong with WLOG? Precisely that you need to translate it! – Count Zero Oct 22 '12 at 15:08
  • Thats why I suggested you translate it to latin, as QED, although you'll probably get some weird look from fellow mathematicians... – Jean-Sébastien Oct 22 '12 at 15:08
  • @Jean-Sébastien: QED has a non-alphanumeric symbol: it's an empty square also called 'tombstone' (I can't insert it here foe some reason). – Count Zero Oct 22 '12 at 15:10
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    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
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    Actually, QED has several non-alphanumeric symbols, including at least $\Box$, $\blacksquare$, $\dashv$ (my favorite), a hollow rectangle oriented vertically, and ▮ (U+25AE), its solid black variant. – Brian M. Scott Oct 22 '12 at 15:23
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    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
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    @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
  • @BrianM.Scott: I didn't mean that reduction to a specific case is generally a bad proof strategy, but you can present it for what it is: our statement will follow easily from its special case where in addition such and such hypothesis is valid; we shall now prove that special case. Doing it once with WLOG is all right, but more than once it gets confusing to justify. – Marc van Leeuwen Oct 22 '12 at 16:53
  • There are symbols for QED because it's useful and aesthetic to give a typographic clue that the proof is over. But when doing scratchwork or boardwork WLOG is succinct enough, and in typescript the words would be written out. – Matthew Leingang Nov 26 '14 at 12:32

3 Answers3

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

Thomas
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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$

quazgar
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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

Count Zero
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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
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    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". – Emily 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
  • (FWIW I didn't vote on WLOG, IIRC) – The Chaz 2.0 Oct 22 '12 at 18:32
  • The problem with introducing a new symbol is that nobody knows what it means. The second problem with introducing a symbol for WLOG is that WLOG itself, by its very nature, puts a burden on the reader simply for the fact that the writer is too lazy, too constrained, or too disinterested in explicitly handling multiple cases in the proof -- or too misguided. WLOG is best used when the extension to generality is obvious (e.g. $|x| > 0$, so WLOG consider $x > 0$), or when the secondary cases have already been demonstrated to be equivalent (in which case WLOG is somewhat redundant). – Emily Oct 22 '12 at 18:53
  • @TheChaz: SODA :P – Count Zero Oct 22 '12 at 21:50