Editing Transfinite induction (section)

{{Short description|Mathematical concept}}
[[File:omega-exp-omega-labeled.svg|thumb|300px|Representation of the ordinal numbers up to <math>\omega^{\omega}</math>. Each turn of the spiral represents one power of <math>\omega</math>. Transfinite induction requires proving a '''base case''' (used for 0), a '''successor case''' (used for those ordinals which have a predecessor), and a '''limit case''' (used for ordinals which don't have a predecessor).]]

'''Transfinite induction''' is an extension of [[mathematical induction]] to [[well-order|well-ordered sets]], for example to sets of [[ordinal number]]s or [[cardinal number]]s. Its correctness is a theorem of [[Zermelo–Fraenkel set theory|ZFC]].<ref>J. Schlöder, [https://jjsch.github.io/output/oa.pdf Ordinal Arithmetic]. Accessed 2022-03-24.</ref>