全能近似分析简介

根据无限的“无有终了”的事实，应当把无尽小数看作无穷数列简写，采用这种观点就可以得到实数的运算法则；如果用康托（Cantor，G）的“无限是现实的、完成了的、存在着的整体”的“实无限”观点就得不到这个法则．点是针对误差界的足够小，其中没有大小的点叫做理想点，有大小的点叫做近似点．理想点具有无法点出的性质．近似点的集合能够组成线段，但理想点的集合不能组成线段．绝对准确地讨论没有大小的理想瞬时上的速度没有实际意义，理想的瞬时速度依赖于近似瞬时的速度．对于点、线、面、实数、函数、导数、积分、积分变换、实数集等数学名词都需要提出近似、理想、全能近似三类技术术语，应用对立统一法则去阐述数学理论．

A Brief Introduction to Omnipotent Approximation Analysis

Acording to the cognition that infinity means ＂have not the end＂, the infinite decimal should be thought as infinite sequence, thus, there is the rule of arithmetical operations for real members. However, acording to Cantor＇s view that ＂infinity is an actual, accomplished, existing whole thing ＂, the same rule would not turn up. All Points are sufficiently small for＇error bounde, among which, Meal point has not a size, while approximate point has a amall size. An Meal point could not be marked off, but a set of approximate points could make up a segment. It makes no sense to aspire after the velocity at a moment which has no size. The ideal instantaneous velocity depends on the velocity at an approximate moment. For mathematical terminologies, such as point, line, plane, real number, derivative, function, integral, integral transformation, etc, three technical terminologeis of approximate, Meal and omnipotent approximation should be put forward, and the mathematics theory should be expounded whith the laws of unity of opposites.