Why is it that given $E=\{ 1, \{2,3\}, \{2,4\} \}$ we have $1\in E$ but $2\not\in E$? I am reading "Book of proof" of Richard Hammard and it says that given the set $E=\{ 1, \{2,3\}, \{2,4\} \}$, we have that $2\not\in E$ . I do not understand why is it so. I understand that the set $E$ is a collection of the elements "$1$", "$\{2,3\}$" and "$\{2,4\}$". But I do not understand why I could not go further and deduce that since $2\in\{2,3\}$ and $\{2,3\}$ is an element of $E$ then $2$ must be an element of $E$.
Sorry if this is a very basic question but I do not even seem to know how to ask for this clarification. 

The set $E$ has exactly three elements: 1, {2,3} and {2,4}. If 2 were an element of $E$, then it would be a fourth element, and we would write $E=\{1,2,\{2,3\}, \{2,4\}\}$. You need to make a distinction between an element such as $2$ and a set that contains exactly one element, such as $\{2\}$.  As another example, $\emptyset$ is the empty set, but $\{\emptyset\}$ is a set that contains exactly one element, and that element is the empty set.
