If a property of an ordinal follows whenever it holds for every smaller ordinal, then it holds for every ordinal.

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Transfinite induction by Wikipedia Bot 1
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Transfinite induction is a generalization of mathematical induction that applies to well-ordered sets, particularly those that are not necessarily finite. It allows statements or properties about all ordinal numbers to be proven by establishing a basis and then using the principle of induction over transfinite ordinals.
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