What is the notation for the number of elements in a set?

Question

Let's say S = {1, 2, 3}. There are 3 elements in S. How do I express this in notation? I tried using google but I could not find what I was looking for.

Answer 1

This is called the cardinality of the set. There are many addition rules, etc. associated with it, but I will not say anything about that here. You can easily search that up on Google. The notation used for the cardinality of a set $S$ is usually one of the following: $$\mathrm{card}(S), \# S, |S|, \overline{\overline{S}}$$ Usually, though, $|S|$ is used (I prefer $\mathrm{card}(S)$, as $|S|$ could, at least in category theory, be mistaken for the geometric realization functor).

Answer 2

As SDevalapurkar said they are a lot of notations for cardinality of a set but I prefer the use of $|S|$ because it is conceptually close (if not the same) to the concept of absolute value that is the norm of dimension 1.