Cleaner notation for cardinality of set instead of |{⋅}| I feel it's a little ugly to use the normal "absolute value" notation for the size of an anonymous set-builder set:
$$
N = |\{ x \in \mathcal{X} : f(x) \geq 0 \}|
$$
Is there a preferred replacement? I feel like I've seen
$$
N = \# \{ x \in \mathcal{X} : f(x) \geq 0 \}
$$
in some informal notes, but I'm not sure if it's used in formal publications.
 A: First off, the "size" of set is not well-defined.  "Size" could refer to any of a plethora of different things, such as cardinality, measure, or diameter.  If you mean "cardinality" (which seems to be the intended meaning, based on the the use of $\#\{x\in \mathcal{X} : f(x) \ge 0\}$), then you should say "cardinality", and not "size".
Assuming that cardinality is the meaning of the notation, then there are several notations which I have seen in the wild (in publications, on the interwebs, etc.):


*

*$\operatorname{card}(A)$ (this is the notation I prefer)

*$|A|$

*$\#A$

*$\mathcal{N}(A)$

*$n(A)$

*$\bar{\bar{A}}$
The notations higher on the list are, I think, somewhat more universal, and more likely to be understood from context.  I would still recommend taking the space to explicitly explain the notation (e.g. "The cardinality of a set $A$ is denoted by $\#A$").
Regarding the use of these notations in formal publication, that is between you and your editor (and/or reviewers).  Pick whichever notation you prefer, and change it if you are asked to by an editor or reviewer.
