V2EX successor ordinal

Successor Ordinal

释义 Definition

后继序数:在序数理论中,若某个序数 α 可以写成 β + 1(其中 β 是某个序数),则称 α 为一个后继序数(successor ordinal),而 β 是它的前驱序数。它与极限序数(limit ordinal)相对。(该术语主要用于集合论与超限归纳等语境。)

例句 Examples

A successor ordinal is one more than some ordinal.
后继序数就是某个序数再加一得到的序数。

In transfinite induction, successor ordinals and limit ordinals are handled in different steps of the proof.
在超限归纳中,证明通常会把后继序数情形与极限序数情形分开处理。

发音 Pronunciation (IPA)

/skssr rdnl/ (AmE 常见)
/skss dnl/ (BrE 常见)

词源 Etymology

successor 源自拉丁语 successor,意为“继任者、后继者”,在数学里引申为“紧接在后、由前一个推进得到的对象”。ordinal 来自拉丁语 ordinalis,与“顺序、次序”相关。合起来在集合论中表示“由某个序数加 1 得到的序数”。

相关词 Related Words

文学与经典著作 Literary Works

  • Thomas Jech, Set Theory(集合论经典教材中常用“successor ordinal / successor”来区分后继与极限情形)
  • Paul J. Cohen, Set Theory and the Continuum Hypothesis(涉及序数与构造层次时常出现相关用语)
  • Wacaw Sierpiski, Ordinal Numbers and the Alephs(专门讨论序数与阿列夫的著作中频繁出现该概念)
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