(Solved): What is the next element of x in the list(1.1) above? Let's let \( y=\emptyset \cup\{\emptyset\} \) ...

What is the next element of x in the list(1.1) above?

Let's let \( y=\emptyset \cup\{\emptyset\} \). Since this \( y \) is in \( x \), the axiom guarantees that \( y \cup\{y\} \in x \), which means \( \emptyset \cup \) \( \{\emptyset\} \cup\{\emptyset \cup\{\emptyset\}\} \) is in \( x \). With repeated application of the Axiom of Infinity, we realize that \( x \) must contain the elements \[ \emptyset, \emptyset \cup\{\emptyset\}, \emptyset \cup\{\emptyset\} \cup\{\emptyset \cup\{\emptyset\}\}, \ldots . . \]