# Opinion on a symbol

I would like to create a new symbol for WLOG (= without loss of generality), since there doesn't seem to be any around. I have some variants and I'd like a 'vote of confidence' on either from the community. Would you close such question? (Before you answer, please take a look at: Is there another symbol that is slightly different from \forall (likewise for \exists)?)

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My opinion is that the symbol should be "without loss of generality", completely spelled out. Symbols such as "for all" are not abbreviations. – egreg Oct 23 '12 at 6:50

I think it's better to ask a specific question like the one you linked to. Something like, "How would I create the following symbol that would represent 'without loss of generality'?":

And then include an image like above, together with a sample usage and possible dimensions. A generic question about the symbol might not lead to it being helpful for future users, since the final choice of the "most helpful" answer could be very subjective. The StackExchange network - in most cases - doesn't works much better in a definitive Q&A style than asking questions that seek generic advice on topics. Perhaps also refer to Don't ask us about best practices, glom of nit, or Mrs Cake.

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Since the title is now "Opinion on a symbol", I'd like to give mine.

Symbols in mathematics are not abbreviations. Using \therefore or \because in a mathematical text is wrong, unless they are used in a formal proof with a well defined meaning. But plain mathematical proofs are usually not formal proof: they should be understandable by the reader and symbols should denote mathematical entities, not linguistic ones.

So I never use \forall or \exists in a proof; sometimes I indulge in a \implies or \iff in a set of displayed formulas, but very sparingly and only when they convey a mathematical, rather than linguistic, meaning.

One of my first duties when converting to LaTeX some papers written by a friend and colleague was

find "w.l.o.g." and replace it with "without loss of generality"

Do a favor to your readers and use words rather than shorthand.

Finally, in a formal proof there's no way of saying without loss of generality: a formal proof must check all possibilities. So even there we can't find a use of a symbol.

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Thanks @egreg - I already got strongly discouraged from doing that at the math.SX site. I saw it recurring in an algorithm description with several agents and the idea is that any agent can make the first move, without changing the overall outcome. I agree, WLOG is rather casual... and I don't really feel comfortable using it. – Count Zero Oct 24 '12 at 9:18
I have to slightly disagree with you. I think that text abbreviations like "w.l.o.g." and "iff" can be used in a mathematical text and don't make it inconvenient. They are well understandable and really common. But I suppose that this may differ from comunity to comunity. – yo' Oct 24 '12 at 11:45
@tohecz "Iff" was invented, IIRC, by Halmos for stating definitions, where the use of "if and only if" would be too heavy. Unfortunately it has since been abused where "if and only if" would be necessary and clearer. – egreg Oct 24 '12 at 11:55
Sigh, for definition, simple if ought to be used imo. – yo' Oct 24 '12 at 11:57
@tohecz Actually no: if is improper (not to say wrong). One should say "X stands for A, B and C" or "X is defined to mean A, B and C" or the like. So the use of a different word is justified. – egreg Oct 24 '12 at 12:01
Incidentally, this idea that symbols are not abbreviations is somewhat field-dependent. It applies in pure mathematics, of course, but in other fields (e.g. physics) such symbols are often used to indicate something similar, but not identical, to their pure mathematical meaning. In any case the issue of whether or when a particular symbol is appropriate is kind of tangential to the main point of the question. – David Z Oct 27 '12 at 3:23

You could define (this assumes that you're using the amsmath package and its \text command):

\newcommand\wlog{\text{\textsc{wlog}}}


Obviously this isn't a symbol (at least not in any sense of the word I'm familiar with), but it would have the advantage of being easily parseable.

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