Proposition 1. Transfinite Induction.
Let $C$ be a class of ordinals. Suppose:
- \[0 \in C.\]
- \[\forall \alpha \in C : \alpha + 1 \in C.\]
For every limit ordinal $\alpha$,
\[\alpha \subseteq C \enspace\rimp\enspace \alpha \in C.\]Then $C = \Ord$.
Proposition 1. Transfinite Induction.
Let $C$ be a class of ordinals. Suppose:
- \[0 \in C.\]
- \[\forall \alpha \in C : \alpha + 1 \in C.\]
For every limit ordinal $\alpha$,
\[\alpha \subseteq C \enspace\rimp\enspace \alpha \in C.\]Then $C = \Ord$.