Difference between Element and Element in braces in set Suppose A = {1,2} B={0,1,{1,2}}
As I understand, A ∈ B, but is A ⊆ B? 
On the one hand all elements of A are also elements of B, but is {1,2} = {{1,2}}?
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''As I understand, A ∈ B, but is A ⊆ B?''
Indeed, $A$ is an element of $B$.
But $A$ is not a subset of $B$. If so, $1,2$ would be elements of $B$, but $2$ is not.

''but is {1,2} = {{1,2}}?''
Nope. $\{\{1,2\}\}$ is a set which contains $\{1,2\}$ as an element. So $\{1,2\}\in \{\{1,2\}\}$.
A: Here's an image of the sets $A$ and $B$:

The points denote the sets, the loops encircle the elements. As you see, the blue dot (set $A$) is in the red circle (belonging to set $B$, thus $A\in B$), but not all dots in the blue circle (the elements of $A$) are also in the red circle (the elements of $B$), as $2\in A$ but not $2\in B$. Therefore $A$ is not a subset of $B$.
And with a picture, you can also easily see that $\{1,2\}$ and $\{\{1,2\}\}$ are different sets:

You see, neither $1$ nor $2$ is an element of $\{\{1,2\}\}$, but both are elements of $\{1,2\}$. So $\{1,2\}$ is neither equal nor a subset of $\{\{1,2\}\}$, but an element of it.
A: Think of a set as a box. 
$A = \{1,2\}$ is a box with two cards numbered $1$ and $2$.
$B=\{0,1,\{1,2\}\}$ is a box with two cards numbered $0$ and $1$ and a smaller box with two cards numbered $1$ and $2$. We can think of it as $B=\{0,1,\{1,2\}\}=\{0,1,A\}$, so $A\in B$.
$A\not\subseteq B$, because $1\in B$, but $2\not\in B$. In other words, the box $A$ has the card $2$, but the box $B$ does not have the card $2$. Instead, the box $B$ has a smaller box with card $2$, so the card $2$ can not be the same (identical) as a box with the card $2$. 
