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

[Swisspick]

Here an example .

 

[HallsofIvy]

{ 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.

 

[JeffM]

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 ....

 

[Dr.Peterson]

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]".