Where can I find a description of math language symbols? I am reading math articles. I meet math symbols.
For example $\exists$ or $\forall$.
For example for "For any a exist e that" can be rewriten as: $\forall a \exists e$
Where can I find full description of this math language?
 A: I think for a "Full Description", you need a textbook, but there are plently of decent resources online.
A rather terse setting out of the symbols used in logical notation exists here:
https://en.wikipedia.org/wiki/List_of_logic_symbols
For a slightly more instructive list, this seems rather good:
http://www.philosophy-index.com/logic/symbolic/
And here's a Symbolic Cheat Sheet:
http://cl.indiana.edu/~md7/15/614/misc/symbols.pdf
But look, I'm basically doing your google search for you - these particular symbols seem to be all to do with Symbolic Logic - if you are studying other areas of math, there will no doubt be other notations, and other resources online for you to discover.
A good resource that enumerates (and, importantly for googling stuff, names) a wide range of math notation is this Latex reference: https://reu.dimacs.rutgers.edu/Symbols.pdf
It sets out all manner of symbols and squiggles, along with the text-command used to render them in Latex. If nothing else, this could provide you with a name to google and learn about the meaning of a specific symbol.
Unhelpfully, depending on the area of math you're studying, there can be "regional" dialects - for example, sometimes, surrounding something with single-bars $|Z|$ can mean taking the absolute value of an expression, but in set notation, it can refer to the cardinality/count of elements in a set. 
Learning the local customs of mathematical notation can take time, but is usually interesting and rewarding.
A: The International Organization for Standardization (aka ISO), has published the ISO 80000-2 which gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications.
The recommendations in ISO 80000-2 are intended mainly for used in the natural science and technology, but also applies to the areas where mathematics is used.
The ISO 80000-2 comes with a cost to reading it but you should be able to find a copy of pdf if you look harder in the internet like I did but this one is published in 2009: https://people.engr.ncsu.edu/jwilson/files/mathsigns.pdf
If you want something freshly published: https://www.iso.org/standard/64973.html
