V2EX non-archimedean

Non-Archimedean

释义 Definition

非阿基米德的;非阿基米德性质的(数学):指某种“大小/距离”的度量不满足阿基米德性质(直观地说:存在“无穷小”或“无限大”的量,或距离满足更强的超度量/非阿基米德不等式),常见于 p-进数、超度量空间、非阿基米德赋值等语境。

发音 Pronunciation (IPA)

/nn kmidin/

例句 Examples

A non-Archimedean field can contain infinitesimals.
非阿基米德的域可以包含无穷小量。

Non-Archimedean geometry studies spaces defined using p-adic distances rather than real-number distances.
非阿基米德几何研究用 p-进距离(而非实数距离)来定义的空间。

词源 Etymology

non- 表示“非……”。Archimedean(阿基米德的)源自古希腊数学家 Archimedes(阿基米德)的名字;“阿基米德性质”是经典实数大小观的一种公理化表达。加上 non- 后,表示“不满足阿基米德性质”的结构或理论。

相关词 Related Words

文学与名著用例 Literary Works

  • p-adic Numbers: An Introduction Fernando Q. Gouvêa
  • Ultrametric Calculus: An Introduction to p-Adic Analysis W. H. Schikhof
  • Non-Archimedean Analysis Serge Lang
  • p-adic Analysis Compared with Real Svetlana Katok
  • Algebraic Number Theory Jürgen Neukirch(涉及赋值与相关的非阿基米德结构语境)
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