I have seen two different common notations for the cardinality of a set:
$\lvert A\rvert$, and $\#A$.
Is there a context in which one is more appropriate than the other? Personally I prefer the latter notation because I think it improves readability when the set in question takes a lot of space to write down:
$$ \begin{align*} \lvert\{x\in X: \exists y\in Y\, \lvert x-y\rvert < 100\}\rvert \\ \#\{x\in X: \exists y\in Y\, \lvert x-y\rvert < 100\} \end{align*} $$
But I also think that it is more intuitive and helps with reducing ambiguity like in the above expression where $\lvert\cdot\rvert$ is being both used as the absolute value and as set cardinality. Is there any reason to use one over the other? I have noticed that the $\#$ notation appears frequently in number theory texts but that is the extent of my exposure to these notations.