$x\in \{\{\{x\}\}\}$ or not? I wonder if we can we say $x\in \{\{\{x\}\}\}$?  
In one viewpoint the only element of $\{\{\{x\}\}\}$ is $\{\{x\}\}$. In the other viewpoint $x$ is in $\{\{\{x\}\}\}$, for example all people in Madrid are in Spain.

No, if it were true it would break many things, for example the set theoretic construction of the natural numbers:
$$ 0 = \emptyset \\
 1 = \{\emptyset\}\\
 2 = \{\{\emptyset\}\}\\
\vdots$$
