Definition 1. Let $\alpha$ be a limit ordinal and $\gamma$ be an increasing $\alpha$-sequence of ordinals. The limit of $\gamma$ is
\[\lim_{\xi \to \alpha} \gamma_\xi = \sup \{\gamma_\xi : \xi < \alpha\}.\]References
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- Thomas Jech. Set Theory. 3rd Millennium ed, rev. and expanded. Springer, 2002. p. 22.