 Normality and argument order in ordinal arithmetic

Ordinal addition, multiplication and exponentiation are continuous in their right argument by recursion. For fixed $\beta$, $\beta +\alpha$ is normal for every $\beta$, $\beta \alpha$ for $\beta >0$, and ${\beta }^{\alpha }$ for $\beta \ge 2$. Reversing the roles changes the conclusion: $\alpha +\beta$ is not normal for $\beta >0$, while $\alpha \beta$ and ${\alpha }^{\beta }$ are normal only for fixed $\beta =1$. Large principal-ordinal limits expose the failures of continuity; constant zero or one cases fail strict increase.