space between \exists and \forall

Question

I'm writting maths papers. I do use a lot of

$ \ exists ; \ forall $

but I have this problem, they glue the next caracter to them. It is really bad for comprehension... So, in my parameter folder, I redefined those two operators like this :

\let\oldexist\exists
\renewcommand{\exists}{\oldexist \ }

but I'm not quit satisfied because, If for instance i'm writting, it exists an unique... there is a space between \exists and !...

Do you have any idea how to solve this problem?

It is not only linked to those two quantificators, but also if I want to write a math sentence, it is hard to make it clear because everything is glued, one to the other... I want it to be more spaced... that it uses more space horizontaly. For instance :

$ A \subset B ; B \subset C $

instead of that : (that's how it appears on the pdf )

$ A \subset B;B \subset C $

\exists and \forall are classified as \mathord (ordinary), ; is a \mathpunct (punctuation), and \subset is a \mathrel (relation, I have no idea what \subspace is). Different classes follow different spacing rules. I don’t recommend changing their behavior as they are by design. — Ruixi Zhang, Jun 29 '18 at 22:44
But you are not helping me. The result is bad... I need to do something about it — Marine Galantin, Jun 29 '18 at 22:45
That’s why I’m leaving a comment rather than an answer. If you want your math to feel like a sentence, then perhaps write a sentence: for all $\epsilon>0$, there exists $\delta>0$ or \[ f(x)\ge0 \quad \text{for all } x>0 \]. Also, check this answer where spaces are added manually depending on the actual situations. — Ruixi Zhang, Jun 29 '18 at 22:51
the spacing of \exists and \forall is set up for the usual use in constructs such as \exists x... as the use here seems to be different the commands could be reclassified (perhaps as \mathop? but I can't really guess the intended meaning of \exists;\forall or how the three characters should be classified? — David Carlisle, Jun 29 '18 at 22:56
Thank you for the link because I have actually the same problem as the guy. The answers are interesting but they do not resolve the core of the problem. So the problem is that the sentence looks cramped and I want that it is made automatic that it isn't. All the answer are unfortunately giving a method to do it by hand, which is I think not the mood of Latex... — Marine Galantin, Jun 29 '18 at 22:56
@MarineGalantin It is unfortunate indeed. Since you used the tag “typography”, I’ll give my take. IMHO, the problem comes from the poor kerning among math typefaces, so it is a problem of design. So, if the designer didn’t/couldn’t account for the spacing, it’s up to the user, which is a common practice when using typefaces for body text in banner/poster titles. See, for instance, A beginner’s guide to kerning like a designer. — Ruixi Zhang, Jun 30 '18 at 06:06
A variant of the @RuixiZhang approach: \text{$A \subset B$; $B \subspace C$.} I’d recommend you look for a different approach, but if you don’t like the default spacing of \exists and \forall, you might try variants with a different spacing class, such as \mathop{\exists} \mathop{\forall}? I’m not clear exactly what you want, though. — Davislor, Jun 30 '18 at 08:41
In my opinion as a professional mathematician you should almost never use \forall and \exists in formal written mathematics. Of course, this comment does not solve the problem you asked about. Rather, I am suggesting that you have a more serious problem because mathematics should not be written this way. This said, if you do want help with this problem then please provide a minimal working example that clearly shows what you are trying to do. — , Jun 30 '18 at 08:59
what I want is quit simple, I don't see the point of writting everytime : , / in order to make it less cramped. My question is how can you override this problem? — Marine Galantin, Jun 30 '18 at 10:33
@Andrew Why not? Would you write them out in English or what? What would you do in mathematical logic? (Well, it depends on notation. Certainly you can do without one or other, if you must and there are, of course, ways of symbolising 'for all' without \forall, so I guess you could do without them. But it would certainly make things less readable.) — cfr, Jun 30 '18 at 23:05

score 3 · Accepted Answer · answered Jun 24 '20 at 15:19

Since the question seems to be very popular and without answer, here I post the solution I am using.

I am comparing my solution to the default behaviour of Overleaf.

default :

$$ \forall x \in B_r, \  \exists a, \ \exists ! y \colon \mathcal P $$
$$  A \subset B;B \subset C $$

mine :

$$ \forall x \in B_r, \  \exists a, \ \existu y \colon \mathcal P $$
$$  A \subset B;B \subset C $$

with this configuration for me :

\let\oldforall\forall
\renewcommand{\forall}{\oldforall \, }
\let\oldexist\exists
\renewcommand{\exists}{\oldexist : }
\newcommand\existu{\oldexist! : }

It relies on having smaller spaces. A reference is here : http://www.emerson.emory.edu/services/latex/latex_119.html

where it is written :

In a math environment, LaTeX ignores the spaces you type and puts in the spacing that it thinks is best. LaTeX formats mathematics the way it's done in mathematics texts. If you want different spacing, LaTeX provides the following four commands for use in math mode:
\; - a thick space
\: - a medium space
\, - a thin space
\! - a negative thin space

I included the line with sets because I mentionned that in the original question. If I would like to put more space, currently I would add \ or \quad.

space between \exists and \forall

1 Answers1