User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-11227630-20170803025655

In the generation of $$C_{n+1}(\alpha,\beta)$$, one needs $$\epsilon\le\eta<\alpha$$. I think $$\epsilon<\alpha\wedge\eta<\alpha$$ is enough to make the induction well-defined, but $$\epsilon\le\eta$$ seems unnecessary.

Why we need $$\alpha\le\beta$$ in $$\Psi_\pi(\alpha,\beta)$$?