# Question about notation in set theory

• I
• DaTario
In summary, the conversation discusses the use of the notation (#) for the number of elements in a set and whether or not it is well known and accepted in scientific communication. The experts suggest alternative notations and offer a helpful resource on writing in professional journals.

#### DaTario

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

# 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

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

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

## 1. What is set notation in set theory?

Set notation in set theory is a way of representing mathematical sets and their elements using symbols and mathematical expressions. It allows for concise and precise communication of concepts in set theory.

## 2. What are the basic symbols used in set notation?

The basic symbols used in set notation include curly braces { }, which enclose the elements of a set, the element-of symbol ∈, which indicates that an element belongs to a set, and the empty set symbol ∅, which represents a set with no elements.

## 3. How is set notation used to define sets?

Set notation can be used to define sets by listing their elements within curly braces, separated by commas. For example, the set of even numbers can be defined as {2,4,6,8,...}.

## 4. What is the difference between set-builder notation and roster notation?

Set-builder notation is a way of defining a set by specifying a rule or condition that its elements must satisfy, while roster notation lists all the elements of a set. For example, the set of even numbers can be defined using set-builder notation as {x | x is an integer and x/2 is also an integer}, while it can be listed using roster notation as {2,4,6,8,...}.

## 5. How is set notation used in operations on sets?

Set notation is used in operations on sets to represent the relationships between sets. For example, the union of two sets A and B can be represented as A ∪ B, and the intersection of two sets A and B can be represented as A ∩ B. It can also be used to express set operations such as complement, subset, and power sets.