MHB What does this vertical line mean after X?

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The vertical line in set-builder notation signifies "for which holds that" or "such that." It indicates conditions for elements in a set, as in "the set of all X for which X is not an element of itself." This notation is essential for defining sets with specific properties. Understanding this terminology is crucial for working with mathematical sets. The discussion clarifies the meaning and usage of the vertical line in this context.
Natalie1
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Hi Natalie! Welcome to MHB! (Smile)

The vertical line means: "for which holds that".
So it reads as: the set of all X for which holds that X is not an element of itself.

It's part of the set-builder-notation.
 
While equivalent to what I like Serena posted, I was taught (in the context of set builder notation) it means "such that." :)
 
Thank you very much! (Smile)
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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