Ordinals under Multiplication form Ordered Semigroup

Theorem

$\struct {\On, \times, \le}$ forms an ordered semigroup, where:

$\On$ denotes the class of all ordinals

$\times$ denotes ordinal multiplication.

Proof

The result follows from Ordinals under Multiplication form Semigroup and Subset is Compatible with Ordinal Multiplication.

$\blacksquare$