Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence
\begin{equation}
X, \quad
\mathcal{P}(X), \quad
\mathcal{P}(\mathcal{P}(X)), \quad
\mathcal{P}(\mathcal{P}(\mathcal{P}(X))), \quad
\ldots
\end{equation}
Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence
\begin{equation}
\mathcal{P}^0(X), \quad
\mathcal{P}^1(X), \quad
\mathcal{P}^2(X), \quad
\mathcal{P}^3(X), \quad
\ldots
\end{equation}
Let $X$ be a D11: Set.
The hyperpower set sequence of $X$ is the D62: Sequence
\begin{equation}
X, \quad
\mathcal{P} X, \quad
\mathcal{P} \mathcal{P} X, \quad
\mathcal{P} \mathcal{P} \mathcal{P} X, \quad
\ldots
\end{equation}
