I am stuck with a small question. It is below,
Let $A$ be a set and let $B = \{A,\{A\}\}$. Then, since $A$ and $\{A\}$ are elements of $B$, we have $A \in B$ and $\{A\} \in B$. It follows that $\{A\}\subseteq B$ and $\{\{A\}\} \subseteq B$. However, it is not true that $A\subseteq B$.$\hspace{302pt}\blacksquare$
I have to ask two questions from this text,
- What is the difference between $A$ and $\{A\}$?
- As $A$ is contained by $B$ so $A$ belongs to $B$ should be true but it is not. Why is that?
Thanks.