What does this vertical line mean after X?

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Discussion Overview

The discussion centers around the interpretation of the vertical line in set-builder notation, specifically in the context of defining sets. Participants explore its meaning and usage in mathematical expressions.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant states that the vertical line means "for which holds that," indicating a specific condition for the elements of the set.
  • Another participant suggests that it is equivalent to "such that," presenting a slightly different phrasing but implying a similar understanding within set-builder notation.
  • A third participant expresses gratitude for the clarification provided.

Areas of Agreement / Disagreement

Participants appear to agree on the general meaning of the vertical line in set-builder notation, though they use different phrasing to describe it.

Contextual Notes

There may be nuances in interpretation based on educational background or context, but these are not fully explored in the discussion.

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)
 

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