TITLE: How to represent "not an empty set"?
QUESTION [22 upvotes]: I'm writing a academic paper and need to represent "A is not the empty set". What is usual way for professional mathematicians?
My idea is: 
$|A| > 0$
However, using the emptyset $\emptyset$ might be more intuitive:
$A\ != \emptyset$
But, I know "!=" is not permissible in math community (only in programmers).
Update
Sorry, I fixed the second equation:
$|A|\ != \emptyset \rightarrow A\ != \emptyset$

REPLY [3 votes]: Let $A$ denote a set.
In constructive mathematics, there's a difference between the statements '$A$ is non-empty,' which is defined to mean that $A$ is not isomorphic to $\emptyset$, and '$A$ is inhabited,' which is defined to mean that $A$ has at least one element, i.e. $\exists a \in A(\mathrm{True})$. Thus, depending on their standpoint and interests, a professional mathematician will probably write one of '$A$ is non-empty' or '$A$ is inhabited.'
Classically, these are equivalent.