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