Ordinals under Addition form Ordered Monoid
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Theorem
$\struct {\On, +, \le}$ forms an ordered monoid, where:
- $\On$ denotes the class of all ordinals
- $+$ denotes ordinal addition.
Proof
The result follows from Ordinals under Addition form Monoid and Ordinals under Addition form Ordered Semigroup.
$\blacksquare$