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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?

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    Mathematical Operators: http://www.unicode.org/charts/PDF/U2200.pdf2012-10-18

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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.