Q:

How does one denote the number of elements of a set $X$?

If I have a specific set of some elements like:
$$X = \{1,2,3,4,5,6\}$$
How can one make an expression for the number of elements of the set $X$? 

A:

You're looking for the cardinality of a set, which is usually denoted by vertical bars:
$$| X |$$

A:

It's common enough to write $\#X$, too.

A:

It is commonly denoted with vertical or double vertical lines: $|X|$ or $||X||$. Once I also saw an accent: $\bar{X}$.

