= Fixed point of a normal ordinal function
{title2=$f(\alpha)=\alpha$}
For a strictly increasing ordinal class function continuous at limits, start with $\alpha_0=0$ and iterate $\alpha_{n+1}=f(\alpha_n)$. If the sequence stabilizes, its stable value is a <fixed point>. Otherwise its supremum $\alpha$ is a limit and continuity gives $f(\alpha)=\sup_n f(\alpha_n)=\sup_n\alpha_{n+1}=\alpha$. Starting the iteration above any prescribed ordinal gives arbitrarily large fixed points.
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