Let $\alpha$ be a limit ordinal and $\gamma$ be an increasing $\alpha$-sequence of ordinals. The limit of $\gamma$ is
\[\lim_{\xi \to \alpha} \gamma_\xi = \sup \{\gamma_\xi : \xi < \alpha\}.\]
Let $\alpha$ be a limit ordinal and $\gamma$ be an increasing $\alpha$-sequence of ordinals. The limit of $\gamma$ is
\[\lim_{\xi \to \alpha} \gamma_\xi = \sup \{\gamma_\xi : \xi < \alpha\}.\]