Is $x\in\{\{x\}\}$ Is $x\in\{\{x\}\}$. I understand that $x\in\{x\}\in\{\{x\}\}$ does this mean $x\in\{\{x\}\}$?
Very simple just unsure about the properties of $\in$, not looking for an extravagant answer, thanks in advance for the help.

The answer is no. $\{\{x\}\}$ has exactly one element, namely $\{x\}$.
In general, to test if $a\in b$, we do the following:


*

*Is $b$ a set?

*If so, is $a$ one of the elements in the set $b$?
$a$ can be a set itself, or not, doesn't matter.
