重建自然数理论

Reconstruction of the Theory of Natural Numbers

摘要: 目的 重建自然数理论，为数学提供一个安全的基础。方法考察自然数概念发生和应用的客观背景及真实过程。结果存在比自然数更为原始的概念。结论①诸多的“1”和遍历运算是数学的初始概念，它们蕴涵现今的自然数理论的所有概念和性质，包括相容性。②算术公理是相容的，但其直接性证明并不存在。

Abstract: The purpose is to reconstruct the theory of natural numbers and to provide a safe basis for mathematics. The method is to observe the objective background and the real process of the occurrence and application of natural numbers. The result is that there is a more primitive concept than the natural number. Conclusions are obtained that ① many “1” and traversal operations are the initial concepts of mathematics, which embody all the concepts and properties of current natural number theories with the compatibility; ② arithmetic axioms are compatible, but their direct proof does not exist.