= Cofinality of a continuous cardinal hierarchy
{title2=$\operatorname{cf}(\beth_\delta)=\operatorname{cf}(\delta)$}
At a nonzero <limit ordinal> $\delta$, a strictly increasing continuous sequence of <cardinals> $(\kappa_\alpha)_{\alpha\le\delta}$ satisfies $\operatorname{cf}(\kappa_\delta)=\operatorname{cf}(\delta)$. A cofinal sequence of indices gives the upper bound. Conversely, bounds for a cofinal <set> of values must have cofinal indices, giving the lower bound. In particular the assertion applies to <Beth numbers>.
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