MHB What does this vertical line mean after X?

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SUMMARY

The vertical line in set-builder notation signifies "such that" or "for which holds that." It is used to define a set by specifying a condition that elements must satisfy. In this context, it indicates the set of all X for which X is not an element of itself. This notation is essential for understanding mathematical sets and their properties.

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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 'My basic understanding of set theory'

If there are an infinite number of natural numbers, and an infinite number of fractions in between any two natural numbers, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and an infinite number of fractions in between any two of those fractions, and... then that must mean that there are not only infinite infinities, but an infinite number of those infinities. and an infinite number of those...
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