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