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transfinite induction

transfinite induction noun: an extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.

Noun

transfinite induction (plural transfinite inductions)

  1. An extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.
    • The validity of the principle of transfinite induction for well-ordered sets enables us to carry out proofs by transfinite induction and definitions by transfinite induction. A proof by transfinite induction is a direct application of the principle when it is required to show that each element of a...1967, Kam-Tim Leung, Doris Lai-chue Chen, Elementary Set Theory, Parts I and II, Hong Kong University Press, page 108
    • 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...
    Synonyms:
    Noetherian induction, structural induction, well-founded induction

transfinite induction meaning in Tamil

transfinite induction in Tamil

மாற்றுமுடிவு உய்த்தறிதல்

Examples of transfinite induction in a sentence

  • The validity of the principle of transfinite induction for well-ordered sets enables us to carry out proofs by transfinite induction and definitions by transfinite induction.1967, Kam-Tim Leung, Doris Lai-chue Chen, Elementary Set Theory, Parts I and II, Hong Kong University Press, page 108:
  • The published version of 1936 had a different proof based on the famous principle of transfinite induction up to the ordinal #92;varepsilon#95;0 by which consistency^([of Peano arithmetic]) followed.2009, Jan von Plato, “Gentzen's Logic”, in Dov M. Gabbay, John Woods, editors, Handbook of the History of Logic, Volume 5: Logic from...

Synonyms of transfinite induction

  • Noetherian induction
  • structural induction
  • well-founded induction

Forms of transfinite induction

pluraltransfinite inductions

Questions about transfinite induction

What does transfinite induction mean?
Transfinite induction means an extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.
What is transfinite induction in Tamil?
Transfinite induction in Tamil is மாற்றுமுடிவு உய்த்தறிதல். See Transfinite induction meaning in Tamil.
How do you use transfinite induction in a sentence?
The validity of the principle of transfinite induction for well-ordered sets enables us to carry out proofs by transfinite induction and definitions by transfinite induction.
What part of speech is transfinite induction?
Transfinite induction is a noun.
What is the plural of transfinite induction?
The plural of transfinite induction is transfinite inductions.

Words near transfinite induction in the dictionary

  1. transfigurest
  2. transfigureth
  3. transfiguring
  4. transfiguringly
  5. transfinite
  6. transfinite induction
  7. transfinite inductions
  8. transfinite number
  9. transfinite numbers
  10. transfinitely
  11. transfinites

Source and license

Adapted from Wiktionary: transfinite induction (page history and authors); transfinite induction (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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