What is the difference between $x$ and $\{x\}$ when $x$ itself is a set? I've already asked this a part of another question, but thought it'd be easier to elaborate a bit more on my concern.
Let $x$ be a set. What is the difference between $x$ and $\{x\}$? I get that the latter is a set consisting of a single element - namely $x$, but what is the difference?
For example, we can have $x$ to be the set $\{1\}$, then $\{x\}=\{\{1\}\}$. Aren't those $2$ expressions the same?
Another problem are the brackets - when we have a set, do we always have to surround him with brackets, for instance, can we have $x$ to be the set $2$?
Thanks a lot

Think of the brackets as a bag you put things in. Then $\{1\}$ is a bag containing the number $1$. But  $\{\{1\}\}$ is a bag containing a bag containing the number $1$. So two bags, one inside the other. These are different. Physically different if you think real paper bags.
