transfinite induction

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(mathematics, set theory) An extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.

日本語の意味

数学や集合論において、超限帰納法は、順序数や基数などの超限な大きさの順序数集合に対して、数学的帰納法を拡張する方法を指す。

英語の意味

(mathematics, set theory) An extension of mathematical induction to well-ordered sets of transfinite cardinality, such as sets of ordinal numbers or cardinal numbers.

このボタンはなに？

By applying transfinite induction, the mathematician proved that every ordinal has a unique Cantor normal form.

超限帰納法を用いて、その数学者はすべての順序数がカントール標準形で一意に表されることを証明した。

詳細

意味（1）

(mathematics, set theory) 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.

詳細

transfinite inductions （ plural ）