$x\in \{\{\{x\}\}\}$ 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.

The answer to your question is no. Note that the set $ \{ \{ \{ x \} \} \} $ has one element, which is $ \{ \{ x \} \} $, not $x$. To say $ x \in \{ \{ \{ x \} \} \} $ means that $x$ is an element of $ \{ \{ \{ x \} \} \} $, implying that $ x = \{ \{ x \} \} $, which is not true if $x$ is a number. 
