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Transfinite recursion theorem

In mathematics, the transfinite recursion theorem says a function can be defined using a recursion over a well-ordered set; for example, N {\displaystyle \mathbb {N} } but also over general well-ordered sets.

Examples, Recursion with the axiom of replacement & Statements

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Recursion with the axiom of replacement

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Transfinite recursion theorem

Nodes11
Edges10
Triples5
Avg. degree1.82
Density0.181818
Components1

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Transfinite recursion theorem

Top relations

related to Statements · 4
Transfinite recursion theorem → If, In, Let, Transfinite
related to Further reading · 1
Transfinite recursion theorem → ProofWiki

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Important terminology

displaystyle recursion function set transfinite theorem alpha ordinal beta well-ordered given since ordinals proof closed element basis axiom induction also

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SubjectPredicateObjectConfidenceSrc
Transfinite recursion theoremrelated to Further readingProofWiki0.60section
Transfinite recursion theoremrelated to StatementsTransfinite0.60section
Transfinite recursion theoremrelated to StatementsIn0.60section
Transfinite recursion theoremrelated to StatementsIf0.60section
Transfinite recursion theoremrelated to StatementsLet0.60section

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