Transfinite induction is an extension of mathematical induction to ordinal numbers. Its correctness is a theorem of ZF, and relies on the fact that the ordinal numbers are well-ordered, and thus a statement that is not universally true for all ordinals must have a minimal counterexample.
Transfinite induction is an extension of mathematical induction to ordinal numbers. Its correctness is a theorem of ZF, and relies on the fact that the ordinal numbers are well-ordered, and thus a statement that is not universally true for all ordinals must have a minimal counterexample.
Source: Wikipedia "Transfinite induction" · CC BY-SA 4.0
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