[Tex/LaTex] space between \exists and \forall


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 :

\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 $

Best Answer

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 :

$$ \forall x \in B_r, \  \exists a, \ \existu y \colon \mathcal P $$

$$  A \subset B;B \subset C $$

enter image description here

with this configuration for me :

\renewcommand{\forall}{\oldforall \, }

\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.