transfinite induction

名词 n.
中文释义

英文释义

名词 n.
  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 well-ordered set A has a property P.[…]To understand the method of definition by transfinite induction some preparation is necessary.

词形变化

transfinite inductions plural
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