Successor Set of Ordinal is Ordinal/Proof 1
Let $\On$ denote the class of all ordinals.
Let $\alpha \in \On$ be an ordinal.
We have the result that Class of All Ordinals is Minimally Superinductive over Successor Mapping.
Hence, by definition of superinductive class:
- $\forall \alpha \in \On: \alpha^+ \in \On$
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers: Theorem $1.2 \ (2)$