V2EX well-ordering

Well-ordering

定义 / Definition

well-ordering(良序;良序关系):一种特殊的“序”(ordering)。在这种排序下,任何非空子集都一定有最小元素。最常见于集合论与序理论中。
(补充:在数学里它通常指“良序关系”;日常英语中不常用。)

发音 / Pronunciation (IPA)

/wlrdr/

例句 / Examples

The natural numbers have a well-ordering under “<”.
自然数在“小于号 <”之下构成一个良序。

Assuming the axiom of choice, every set can be given a well-ordering.
在选择公理成立的前提下,任何集合都可以被赋予一种良序。

词源 / Etymology

well-(“良好地/完善地”)+ ordering(“排序/序关系”)构成。order 一词源自拉丁语 ordo(“排列、秩序”)。在数学语境中,“well-”强调这种序具有强性质:任意非空部分都能找到最小元

相关词 / Related Words

文学与经典作品用例 / Literary & Notable Works

  • Naive Set Theory(Paul R. Halmos,《朴素集合论》)
  • Set Theory and the Continuum Hypothesis(Paul J. Cohen,《集合论与连续统假设》)
  • Principia Mathematica(Whitehead & Russell,《数学原理》)
  • Contributions to the Founding of the Theory of Transfinite Numbers(Georg Cantor,康托关于超限数理论的经典论文与汇编)
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