What does this symbol mean in this context (#)

Question

Let D ⊆ R and let f:D→R. Assume that #D ≥ 4. Assume that f is strictly 4-monotone, i.e., assume, for all S ⊆ D, that [ #S = 4 ] ⇒ [ (f|S) is strictly monotone ]. Show that f is strictly monotone.

Answer 1

Cardinality: if a set is finite, it means the number of elements of the set.

Another (more common, in my experience) notation for this, if $A$ is a set, is $|A|$.

Answer 2

It refers to the cardinality of $D$ (number of elements in $D$).