Applications of set theory to abstract harmonic analysis

集合论在抽象调和分析中的应用

• 批准号: RGPIN-2017-05712
• 负责人: Steprans, Juris
• 金额: $ 2.19万
• 依托单位: York University
• 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=635264
• 关键词: Applications; set; theory; abstract; harmonic

The reasons for the remarkable effectiveness and applicability of mathematics have been the subject of various philosophical considerations, but the question becomes even more difficult when the use of extra mathematical axioms come into play. How could an axiom whose truth is not easily verifiable have any influence on practical mathematical matters such as those one encounters in physics or finance? But anyone who thinks there can be no such influence should consider an axiom that is often used without further consideration in mathematics, the axiom of infinity. All that the axiom of infinity says is that the set of all natural numbers exists; not that each natural number exists on its own, but that the set of all of them exists as a mathematical object.

数学有效性和适用性的原因一直是各种哲学考虑的主题，但是当使用额外的数学公理开始发挥作用时，这个问题变得更加困难。一个公理如何不容易验证的公理会对实际数学问题（例如物理或金融遇到的人）有任何影响？但是，任何认为没有这种影响的人都应该考虑一个经常使用的公理，而无需进一步考虑数学，即无穷大的公理。无限的公理表明，所有自然数的集合都存在。并不是说每个自然数量都存在，而是它们的集合作为数学对象存在。