Question about notation in set theory

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Discussion Overview

The discussion revolves around the notation (#) used to denote the number of elements in a set, particularly in the context of set theory. Participants explore whether this notation is widely recognized and if it requires explanation in scientific communications.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that (#) is a standard symbol for number, though its use in the specific context described is not commonly seen.
  • Alternatives to (#) are proposed, including |N|, ord(), and card(), with suggestions that these might be more appropriate, especially in formal settings.
  • One participant expresses a personal opinion that providing a brief explanation of the (#) notation would be beneficial in scientific writing.
  • Concerns are raised about the potential confusion caused by the dual use of | in notation, suggesting that clearer alternatives should be used.
  • A participant mentions that the (#) notation was found in the works of Paulo Ribenboim, indicating that it may not be universally accepted or recognized in formal contexts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the acceptance of the (#) notation, with some advocating for its use and others suggesting alternatives. The discussion remains unresolved regarding the necessity of explaining this notation in scientific communications.

Contextual Notes

There are varying opinions on the appropriateness of different notations for cardinality, and the discussion highlights the potential for confusion with existing symbols. The context of usage and audience familiarity with the notation are also considered.

DaTario
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Hi All,

Sorry, to begin with, if the question seems to be out of place. My question has to do with the notation (#) for the number of elements in a set:

$$ N = \# \{ v_i \in V \vert v_i v_j \in E \} $$

Is it well known? If written in a scientific communication, must one offer a description of its meaning?

Best Regards,
DaTario
 
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# is a standard (not particularly in mathematics) symbol for number. I have never seen it in the context you describe.
 
DaTario said:
Hi All,

Sorry, to begin with, if the question seems to be out of place. My question has to do with the notation (#) for the number of elements in a set:

$$ N = \# \{ v_i \in V \vert v_i v_j \in E \} $$

Is it well known? If written in a scientific communication, must one offer a description of its meaning?

Best Regards,
DaTario
There are also sometimes notations like ##N = | \{ v_i \in V \vert v_i v_j \in E \}|## or ##N = ord(\{ v_i \in V \vert v_i v_j \in E \})##, especially for groups, or even ##card(\{ v_i \in V \vert v_i v_j \in E \})## for cardinality, which might be better if different orders of infinity are regarded. I think (personal opinion) a short note on what # will denote cannot be wrong. And by the way: I would index ##N_j## with ##j## for its dependent of the choice of ##v_j##.
 
To extend what fresh_42 said, |N| would probably suffice, provided that the definition of set N has been given.
 
fresh_42 said:
##| \{ v_i \in V \vert v_i v_j \in E \}|##

This notation is usually discouraged in professional journals because of the two distinct uses of |. So either you find another notation for cardinality, or you can use

[tex]| \{ v_i \in V ~ : ~ v_i v_j \in E \}|[/tex]

https://www.austms.org.au/Publ/JAustMS/JAustMS_writing.pdf number 14.
 
Thank you all, for the help. In fact, this notation was used by Paulo Ribenboim in his books on number theory. However, as in some of his (really good) books the language is rather informal, I was afraid of not being this notation wide spread or scientifically accepted.

Best wishes,

DaTario
 

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