transfinite induction
短语词形变化
transfinite inductions
复数
transfinite inductions
释义与例句
n.
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1.
An extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.
数学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.