ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D673
Von Neumann ordinal sequence
Formulation 1
Let $\emptyset$ be the D13: Empty set.
The Von Neumann ordinal sequence is the D62: Sequence \begin{equation} \mathcal{P}^0(\emptyset), \quad \mathcal{P}^1(\emptyset), \quad \mathcal{P}^2(\emptyset), \quad \mathcal{P}^3(\emptyset), \quad \ldots \end{equation}
Formulation 2
Let $\emptyset$ be the D13: Empty set.
The Von Neumann ordinal sequence is the D62: Sequence \begin{equation} \emptyset, \quad \mathcal{P}(\emptyset), \quad \mathcal{P}(\mathcal{P}(\emptyset)), \quad \mathcal{P}(\mathcal{P}(\mathcal{P}(\emptyset))), \quad \ldots \end{equation}