What does { x | x .... } mean?

{ x|.....} means the set of all values of x that satisfy condition ...

My German isn't the best but I would say that "M" consists of all values of x that satisfy all of conditions \(\displaystyle E_1\), \(\displaystyle E_2\), \(\displaystyle E_3\), …, to \(\displaystyle E_n\).

For an English example, {x| x^2= 4} is just {-2, 2} since -2 and 2 are the only numbers whose squares are equal to 4.
 
My German ist ganz verloren aber | is used to mean "such that" is many English texts.

So I think it means "If x is in M, x has the properties ....
 
I don't think I'd noticed this until now, but the vertical bar here is very similar to the vertical bar in P(A | B): As that means "the probability of A given B" (that is, assuming that B is true), {x | [statements]} means "the set of x given that the statements are true". Of course, we actually say it as "the set of all x such that [statements]".
 
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