Back Transfinitní indukce Czech Transfinite Induktion German Transfinia indukto Esperanto Inducción transfinita Spanish استقرای ترامتناهی Persian Transfiniittinen induktio Finnish Récurrence transfinie French אינדוקציה טרנספיניטית HE Transzfinit indukció Hungarian Induzione transfinita Italian

Transfinite induction

Representation of the ordinal numbers up to . Each turn of the spiral represents one power of . 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-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness is a theorem of ZFC.[1]

  1. ^ J. Schlöder, Ordinal Arithmetic. Accessed 2022-03-24.

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