How is $\{\emptyset,\{\emptyset,\emptyset\}\} = \{\{\emptyset\},\emptyset,\{\emptyset\}\}$? I'm slightly confused as to how 
$$\{\emptyset,\{\emptyset,\emptyset\}\} = \{\{\emptyset\},\emptyset,\{\emptyset\}\}$$
are equivalent. I thought two sets were equivalent if and only if "$A$" and "$B$" have exactly the same elements. In this case, we have one element which is in both sets but then two elements aren't in other! Can someone please explain where I am going wrong in my definition? 
Thanks a bunch!

may be it is better to use that $\{ \emptyset, \emptyset\} = \{\emptyset\} \cup \{\emptyset\}$
