Category:Ordinal equals its Initial Segment

This category contains pages concerning Ordinal equals its Initial Segment:

Let $\On$ denote the class of all ordinals.

Let $<$ denote the (strict) usual ordering of $\On$.

Let $\alpha$ be an ordinal.

Then $\alpha$ is equal to its own initial segment:

$\alpha = \set {\beta \in \On: \beta < \alpha}$