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An extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences, set-theory
Examples
- 1970 [Addison-Wesley], Howard DeLong, A Profile of Mathematical Logic, Dover, 2004, page 218, Just what kinds of transfinite inductions are to be considered finitary is debatable. Transfinite induction up to an arbitrary ordinal is certainly not finitary. However, it can be shown that certain transfinite inductions are reducible to ordinary mathematical inductions. For example, induction up to ω^ω is reducible to ordinary induction. Gentzen in his proof used transfinite induction up to ε0.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
No etymology was provided for this word.
Across languages
Translations
4 source translations are retained for this English entry.
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German:
transfinite Induktion
— extension of mathematical induction to well-ordered sets of transfinite cardinality
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Hungarian:
transzfinit indukció
— extension of mathematical induction to well-ordered sets of transfinite cardinality
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Italian:
induzione transfinita
— extension of mathematical induction to well-ordered sets of transfinite cardinality
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Portuguese:
indução transfinita
— extension of mathematical induction to well-ordered sets of transfinite cardinality
