ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Transitive set
▼ Ordinal number
▼ Class of ordinal numbers
Definition D1944
Strict ordinal number ordering relation
Formulation 0
Let $\mathsf{Ord}$ be the D686: Class of ordinal numbers.
The strict ordinal number ordering relation is the D4: Binary relation \begin{equation} \{ (\alpha, \beta) \in \mathsf{Ord} \times \mathsf{Ord} \mid \alpha \in \beta \} \end{equation}