Consider a normal operation assigning $t_\alpha$ to each ordinal number $\alpha$, and assume that $\lambda$ is a limit ordinal.
Show that cf $t_\lambda$ $=$ cf $\lambda$.
I want to show that the smallest cardinal $\kappa$ such that $\lambda$ is the supremum of $\kappa$ smaller cardinals is equal to the cofinality of the operation. Help would be appreciated here. I know the cofinality of any ordinal $\alpha$ is the least cardinal number $\kappa$ such that there exists a subset $S$ of the ordinal $\alpha$ having cardinality $\kappa$ and that $\alpha$ is the least ordinal $\textit{strictly}$ greater than every member of $S$ (the strict supremum of $S$).