Distributive law for ordinal multiplication
= Distributive law for ordinal multiplication
<Ordinal multiplication> is distributive in its right argument:
$$
\alpha(\beta+\gamma)=\alpha\beta+\alpha\gamma.
$$
Indeed a sequence of copies of $\alpha$ indexed by the concatenation of $\beta$ and $\gamma$ is the concatenation of the two sequences of copies. The other distributive law fails: $(1+1)\omega=\omega$, while $\omega+\omega>\omega$.