= 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 $\beta\geq2$. 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.
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