Analysis on non-Archimedean field extensions of the real numbers

实数的非阿基米德域扩展分析

• 批准号: RGPIN-2017-04965
• 负责人: Shamseddine, Khodr
• 金额: $ 1.02万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635216
• 关键词: Analysis; non; Archimedean; field; extensions

The field of real numbers R plays a fundamental role in Mathematics and the sciences due to certain special properties. The field is Archimedean: if x,y in R are such that 0 <|x| <|y| then we can find a positive integer n such that n|x| > |y|. This property of R corresponds to common sense experiences of measurement; but the Archimedean axiom breaks down at the Planck scale, i.e. for distances less than 1.6x10

实数领域R由于其特殊的性质在数学和科学中起着重要的作用。这个场是阿基米德式的：如果R中的x，y满足0 <|x| <|y|，那么我们可以找到一个正整数n满足n|x| > |y|。R的这个性质对应于测量的常识性经验；但阿基米德公理在普朗克尺度下就失效了，即距离小于1.6x10