Understanding the use of brackets in set theory notation I would appreciate help understanding the presence and absence of brackets in this particular example, which hopefully will clarify things for me.
It is a line from a short proof by contradiction based on the Axiom of Foundation that No Set is an Element of Itself. 
Why are there brackets on some $S$'s and not on others.


Suppose $S\in S$. Let $T=\{S\}$, then $T\bigcap S=\{S\}$, etc.


Thanks

Let $$E=\{\{a\},\{a,b\}\} $$
then
$$a\in \{a\} \subset \{a,b\} \in E $$
