Talk:Continuous function (ordinal theory)

References to Th. Jech don't match.

Found in "Thomas Jech. Set Theory, 3rd Millennium ed, 2002, 4th printing, 2006, Springer Monographs in Mathematics, Springer-Verlag, Berlin Heidelberg, 1997,2003 ISBN 3-540-44085-2, ISSN 1439-7382, p.22"

Definition 2.17. Let α > 0 be a limit ordinal and let {γξ : ξ < α} be a nondecreasing sequence of ordinals (i.e., ξ < η implies γξ ≤ γη). We define the limit of the sequence by limξ→α γξ = sup{γξ : ξ < α}. A sequence of ordinals {γα : α ∈ Ord} is normal if it is increasing and continuous, i.e., for every limit α, γα = limξ→α γξ. 2A02:A03F:C91A:6600:6DC1:2246:ED4E:A726 (talk) 14:31, 11 June 2025 (UTC)