# Category:Ordinal equals its Initial Segment

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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:

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

## Pages in category "Ordinal equals its Initial Segment"

The following 2 pages are in this category, out of 2 total.