I was tasked to write the following by listing the elements between braces, $$\{X\subseteq\mathscr{P}(\{1,2,3\}): |X|\leq 1\}$$ $\{\emptyset \}$

My textbook gives the solution: $$\big\{\emptyset, \{\emptyset\}, \{\{1\}\}, \{\{2\}\}, \{\{3\}\}, \{\{1, 2\}\}, \{\{1,3\}\}, \{\{2,3\}\}, \{\{1,2,3\}\} \big\}$$

I got everything except the elment $\{\emptyset\}$. What's the difference between $\emptyset$ and $\{\emptyset\}$? Isn't $\emptyset=\{\}$, and likewise $\{\emptyset\}=\{\{\}\}$ which should be equivalent to $\{\}$?