What is the meaning of the square brackets in theorem 8.6.30 (Introduction to Graph Theory) book?

Question

In the book (Introduction to Graph Theory) by Douglas West , what is the meaning of the square brackets in $|[ S , \overline{S} ]|$ ?

Answer 1

That text book has the Answer on Page 152 :

"Given $S , T \subset V(G)$ , we write $[S , T]$ for the Set of Edges having one End-Point in $S$ and the other in $T$.
An Edge Cut is an Edge Set of the form $[S , \overline{S}]$ , where $S$ is a Non-Empty Proper Sub-Set of $V(G)$ and $\overline{S}$ denotes $V(G) - S$."

Concisely , the Author later states that "It is the set of edges joining a vertex in $S$ to a vertex not in $S$" , which is very Intuitive.

More-over , it is standard convention / notation to use $|A|$ to indicate Size of Set $A$.

Hence , $|[S , \overline{S}]|$ indicates "the Size of the Edge Cut" , while that theorem is giving a lower Bound on this Size.

Here is that Page with more Detail :