潜无穷与实无穷相遇大学校园中

去年8月10日，我们向全国普通高校轮番投放实无穷小微积分教科书，这是促进高校微积分教学改革，提升教育质量，培养大批优秀人才的具体行动。

此举使得潜无穷与实无穷相遇大学校园中，发生激烈观念碰撞，互不相容。

    众所周知，潜无穷极限理论根本不承认实无穷小的存在性，对实无穷小百般诅咒、中伤。

    新年始，哥德尔倡导的实无穷小军军团，高举“知识共享”旗帜，吹响冲锋号，向着潜无穷猛冲。

    什么是潜无穷与实无穷？请看本文附件。

袁萌  陈启清  元月6日

附件：

A Comparison of Potential Infinity and Actual Infinity

 Thresiamma N.J

Assistant Professor, Vimala College, Thrissur-9, Kerala, India

Abstract: Infinity is a useful concept of a process with no end. Sometimes its presence is explicit, sometimes it’s not explicit. Mathematicians consider two types of infinities, potential and actual infinity. The main purpose of this paper is to compare actual infinity and potential infinity.

Keywords: Actual infinity, potential infinity, infinitesimal, bigbang theory, steady state theory.

“Mathematical infinity is taken from reality, although uncon sciously and therefore it can only be explained from reality a nd not from itself or from mathematical abstraction.”[1]   

The concept of infinity appears in almost every field of mathematics. Sometimes its presence is explicit, sometimes it’s not explicit. Arithmetic and classical algebra deal with numbers. All the numbers taken together form infinite collections. In geometry, we encounter points on a line, lines on a plane, planes in space. These are not infinite in number, but are also in extent. The core concepts in Mathematical analysis are

limits, continuity, sequences, series, differentiation, integration etc. All these deals with infinitely  large quantities and infinitely small quantities. The infinitesimal have been used to express the idea of objects so small that there is no way to see them or measure them. 

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Mathematicians consider two types of infinities, potential and actual infinity. Potential infinity was accepted as a legitimate mathematical object by mathematicians and logicians. But actual infinity is not accepted until George cantor defined the concept. In schools, teachers try to convince students 0 1 is infinity(strictly for mathematicians

0 1

（以下省略，参阅“无穷小微积分”）

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