Question about notation in set theory

• I
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

mathman
# is a standard (not particularly in mathematics) symbol for number. I have never seen it in the context you describe.

fresh_42
Mentor
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##.

Mark44
Mentor
To extend what fresh_42 said, |N| would probably suffice, provided that the definition of set N has been given.

##| \{ 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

$$| \{ v_i \in V ~ : ~ v_i v_j \in E \}|$$

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