学生们关于欧阳耿的帖子

学生们11

刚才忘了说，我已经在这里2次贴出想请你解决的“究竟如何用极限论处理该调和级数发散性证明中所谓的“无穷小”问题”，真的希望你能去看一看，试试能不能解决。

elim

学生们11 发表于 2015-2-20 19:27
elim先生：从你在这里的一些发言，知道你和欧阳耿在康托的连续统不可数的证明问题上好像有过争论，并且你对 ...

我觉得你好像还没有健全的判断能力。例如你的所谓仇恨从何说来？ 哪句话让你得出这种结论？ 我是心平气和地说他是个学术骗子，痞子的，不是出于个人义气。

还是看看这里吧 http://www.mathchina.com/bbs/for ... p;tid=7882#lastpost
我要这种完整的文章，而且最好要网友看得懂的形式。你贴出的东西版面实在太差，错别字不少。能不能改一改？ 从上面的连接可以看到，我跟他对过话，只是他被点到要穴就装孬而已。

关于无穷小，虽然人们还会在平常的授课，分析讨论上提到它，但严格地说它已经不属于经典分析了。人们使用它就像军官们说要拿下这个山头，或者骂几句娘那样，不属于军事科学。也不会用于论证。十七世纪后半叶到十八世纪初建立起来的数学基础根本不需要无穷小这种既不是0又可以根据需要被忽略的精灵。这个基本了解对你有帮助吗？

既然你真想讨论调和级数的那篇文章，就像像样样把它全文贴出来。最起码不能让他有机会说这不是他的文章，或者那是断章取义。

学生们11

1，好吧那我就把欧阳耿在Research Gate上传的6篇论文和由他所开设的12个数学基础讨论专题贴上去，这些比较规范。这是他自己上传的，我转到这里很正常，我不想无故伤害人家。
2，我不想把欧阳耿在CNKI上的东东贴到这里，因为怕别人误会我在搬弄是非，还是哪句话，我不想无故伤害人家。你为什么不自己到CNKI上面去挑。
如果是你自己贴出来，想怎么批他，骂他（比如：学术骗子，痞子的……），跟我们这种学生哥一点关系都没有。
看到欧阳耿在RG学术讨论网上传的6篇文章和与无穷相关的数学基础12个讨论主题。
1， “A Newly Constructed Infinitude System” ------Forty-year Work in the Infinitude Related Foundation of Mathematics
2，2014 ICM Abstract for OUYANG Geng’s 25 papers
3，A Revolution in the “Infinite” Related Foundation of Mathematics-------“New infinite notion --new infinite number system--new limit theory” and Solving “Infinite Paradox Syndrome”
4，On Limit Theory
5，Four Errors in Cantor’s Proofs on the Uncountability of Real Number Set and the Defects in the Infinitude Related Foundation of Mathematics
6，A New Way Out of Pending Problem in Mathematics
1，Is the divergent proof of Harmonic Series a modern version of Zeno’s Paradox?
The problem disclosed by Zeno’s Paradox is still there and the exactly same idea is still working well. Let’s see one of the modern versions of Zeno’s Paradox
1＋1/2 ＋1/3＋1/4＋．．．＋1/n ＋．．．                                                      （1）
=１＋1/2 ＋（1/3＋1/4 ）＋（1/5＋1/6＋1/7＋1/8）＋．．．                              （２）
>1+ 1/2 ＋( 1/4＋1/4 )+（1/8＋1/8＋1/8＋1/8）＋．．．                                     （3）
=1+ 1/2 + 1/2 + 1/2 + 1/2 + ．．．------>infinity                                                （4）
                                 
Such an antique proof (given by Oresme in about 1360), though very elementary, can still be found in many current higher mathematical books written in all kinds of languages.
Because of the fundamental defects in present classical infinite relating science system, the unavoidable practical problem has been troubling us ever since is how many items in infinite decreasing Harmonic Series can be added up by “brackets-placing rule" to produce infinite numbers each bigger than 1/2?
This kind of “infinite relating paradox” tells us:
1, in Harmonic Series, we can produce infinite numbers each bigger than 1/2 or 1 or 100 or 100000 or 10000000000 or… from infinite infinitesimals in Harmonic Series by “brackets-placing rule" to change an infinitely decreasing Harmonic Series with the property of Un--->0 into any infinite constant series with the property of Un--->constant or any infinitely increasing series with the property of Un--->infinity;
2, the “brackets-placing rule" to get 1/2 or 1 or 100 or 100000 or 10000000000 or… from infinite items in Harmonic Series corresponds to different runners with different speed in Zeno’s Paradox while the items in Harmonic Series corresponds to those steps of the tortoise in Zeno’s Paradox. So, not matter what kind of runner (even a runner with the speed of modern jet plane) held the race with the tortoise he will never catch up with it.   
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2,  Can anyone express self-justification theoretically and practically what infinite is ?
If not, “How can we introduce the idea of infinite to students? Its properties, relationship with zero etc?” So, our students will never know what infinite is and our students’ students will never know what infinite is…., this is a tragedy!
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3，What is “infinite”, why people never stop the debates between “potential infinite” and “actual infinite” ?
“Infinite”, “potential infinite”, “actual infinite”, “potential infinitesimal”, “actual infinitesimal”, “potential infinite-big”, “actual infinite-big”, “Infinite related numbers”,…; What are they?
Some people insist we can we have only one definition of “infinite” in science but others argue that we can have many definitions of “infinite” with different natures in science (at least two: “potential infinite” and “actual infinite”), what can we do?     
1, How many definitions of “infinite” with different natures in science can we have as ideas of human mind?
2, How many definitions of “infinite” with different natures in science can we have as something we can find in the real world?
3，How many definitions of “infinite” with different natures can we have as co-product of human mind and objectivity in science?
4, can we really have many different definitions with different natures for the concept of “infinite” in human science and how can we distinguish them theoretically and practically?
There are many arguments on “infinite-finite” in RG, but we can see they actually are the debates between “potential infinite” and “actual infinite”. Without knowing what “finite-infinite” and “potential infinite-actual infinite” are philosophically and mathematically, these debates will last forever.
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4，what is science, how can we distinguish science from beliefs, experience, culture…?  2014-11-8      If we call our cognizing fruits “knowledge”, they can be science, religious, experience, culture… But our science history tells us that different kinds of cognizing fruits are very often confused (such as taking beliefs or experience or culture as science) thus producing ill influences to our scientific researches.
Should human science be a balance and harmonious compound of "objective and subjective" or "ontology and form" or "truths and representations" or "completeness and Incompleteness" or " inborn and postnatal" or "infinite and finite" or "universe law and the carries of universe law" or …?
If we are not sure what science is, it makes many scientific discussions impossible to go deep and end up fruitless.
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5, Is it possible to integrate three schools of intuitionism, formalism and logicism into one, why and how?
This work will help us re-understand the essences of the three schools and have a better understanding of “what mathematics is”-----to improve our fundamental researches especially in the infinite related area.
From many arguments between and among three schools of intuitionism, formalism and logicism, we understand that they three are all important in the foundation of mathematics. But the cutting apart of the three produces some negative effects (such as placing particular emphasis on one aspect but negate the others,…) which deeply influence our clear understanding of “what mathematics is”, especially in the infinite related area.
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6，Cognition! Is human science like a kind of “living creature”?
Examining our human science, we can see science is very much like a kind of “living creature” -------birth, metabolism, growth, healthy, sick, recover, death or grow into branches and big tresses, …. How do these happen?
  How is the metabolism process of human science going on?
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7， What is limit theory, does limit theory need basic theory, what is it?
There are two reasonable limit operations in present science theory system:
（1） During the whole process in dealing with infinite substances (infinitesimals) in limit calculations, no one dare to say “let them be zero or get the limit”. So, the infinitesimals in the calculating operations would never be too small to be out of the calculations and the calculations dealing with infinitesimals would be carried our forever. This situation has been existing in mathematics since antiquity------ those items of Un--->0 never be 0 all the time and Harmonic Series is divergent, so we can produce infinite numbers bigger than 1/2 or 1 or 100 or 100000 or 10000000000 or… from infinite Un--->0 items in Harmonic Series and change an infinitely decreasing Harmonic Series with the property of Un--->0 into any infinite constant series with the property of Un--->constant or any infinitely increasing series with the property of Un--->infinity. Here we have one of the modern versions of ancient Zeno’s Paradox.
（2） During the process in dealing with infinite substances (infinitesimals) in limit calculations, someone suddenly cries “let them be zero or get the limit”. So, all in a sudden the infinitesimals in the calculations become too small to stay inside the calculations, they should disappear from (be out of) any limit calculation formulas immediately. This situation has been existing in mathematics since antiquity-------those items of Un--->0 must be 0 from some time and Harmonic Series is not divergent, so we cannot produce infinite numbers bigger than 1/2 or 1 or 100 or 100000 or 10000000000 or…from infinite Un--->0 items in Harmonic Series. But if it is convergent, another paradox appears.
But when and why should or should not people treat infinitesimals appearing in infinite numeral cognitions that way? Does limit theory need basic theory, what is it?
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8, What is number? Why and how does it come, how does it exist, and how many number forms do we have so far?
No mathematics without numbers; so, we have many different kinds of numbers in our mathematics to help us cognize all kinds of things in universe.
We have many different kinds of number forms: 0 (zero), natural number, fuzzy number, …, but at the time when they were born in our science, must they be proved mathematically or just came out as needed and staying there without proof?      
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9，        Can the “non-standard analysis” related theory solve those defects disclosed by the suspended infinitesimal paradox family?  
We focus on the “deep structural relationship” between “nonstandard one” and “standard one”. Let’s exam following facts:
1, as “monad of infinitesimals” has much to do with analysis; nonstandard analysis is much more a way of thinking about analysis, as a different analysis------simpler than standard one.
2, CONSERVATIVE is the nature and a must for Nonstandard Analysis or Nonstandard Mathematics, it is called a conservative extension of the standard one.
3, because of the “deep structural CONSERVATIVE”, the “provable” equivalence are guaranteed.
If there are “no defects” in the “standard one”, the “CONSERVATIVE guaranteed nonstandard” work would be really meaningful.
Now the problem is “nonstandard one” inherits all the fundamental defects disclosed by “infinite related paradoxes” from “standard one” since Zeno’s time 2500years ago------guaranteed by the “deep structural CONSERVATIVE” .
Theoretically and operationally, “nonstandard one” is exactly the same as those of “standard one” with suspended infinite related defects in nature. Simpler or not weights nothing here.
10，        What is 0 (zero), different roles, different positions?  
People believe that 0 (zero) has played different rolls as a kind of special form of number (substantiality) in our science, such as:
(1) a kind of reference ------- generator, middle, neutral, beginner, origin, marker,…,
(2) absolutely non-existent ------- without numerical value meaning, the negation of being, objectively nothingness,
(3) relatively non-existent ------- with numerical value meaning, subjectively nothingness, the approximate nothingness, the result of infinitesimal limit , ….
Following three questions are important for us to understand what 0 (zero) is:
1, How does 0 (zero) exist as mathematical language with or without numerical value meaning itself?
2, What position dose 0 (zero) locate in the categorical spectrums of numbers?
3, Do we need a negation of 0?
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11, What are “potential infinite” and “actual infinite”? Is there anything wrong with our understanding and the definitions to “infinite”?   
“Potential infinite” and “actual infinite” are really there in our mathematics and science, but it seems very difficult to understand and express these two concepts clearly and logically ever since.
Why many researchers (such as researchers taking mathematics as a practical tool) refuse “potential infinite” but only accept “actual infinite”. Do we really need both “potential infinite” and “actual infinite” or just need “actual infinite”? Is there anything wrong with our understanding and the definitions to “infinite”?
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12,  What are infinitesimals------- a 2500-year suspended problem?
People may have different names for ”the infinite related very small numerical things (infinitesimals)”, it doesn’t matter what they are called, they are there in our mathematics, but what are their positions as numbers or non-numbers or something else theoretically and practically, ontologically and formally?
The newly discovered modern Harmonic Series Paradox is one of family members of ancient Zeno’s Paradox, it discloses relentlessly a fact that we human still don’t know what infinitesimals are!
This problem has close relationship with whole fundamental part of infinite related area in our mathematics:
1, theoretical and practical infinite concept system
2, theoretical and practical infinite related number system
3, theoretical and practical infinite related number treating system

elim

好，我明天抽时间弄弄这个。

elim

为了让更多的人可以参与讨论，我把欧阳耿的一篇关于“调和级数悖论”的中文文章贴在上面。读一篇没有多大价值的文章，或者胡扯连篇的文章不是什么享受，没有享受连读也不能“一气哈成”，加上欧阳耿错误多产不好处理，不如顺着段落揭开欧阳耿的面纱。欧阳的英文文章中提到而在这里没有处理的部分，如果有的话，稍后再议。

0. “...在传统的有穷-无穷理论体系中，人们永远不可能解决芝诺通过悖论要求人们解决的问题，并且永远无法制止新的芝诺悖论翻版的产生。”

如果欧阳耿认同“饰人之心, 易人之意, 能胜人之口, 不能服人之心”的悖论释义，那么他大可不必写文章论证人们永远无法制止“芝诺悖论”的翻版的产生。脑袋有问题的人是没有穷尽的，任何理论到这等人那里都可能有“饰人之心, 易人之意, 能胜人之口, 不能服人之心”之感，于是都可视作悖论。因此有必要略微澄清一下现代数学悖论的概念。

悖论是蕴含矛盾命题的数学构造。我们尽可能不进入专业的数学基础内容的深入介绍和论证，粗略地说，我们约定数学是由元词（原始数学对象，原始关系），元谊（公理即逻辑值为真的原始命题），逻辑连词，量词，语句构成法则等生成的语言集成，其中包括全部集合论ZFC的元词和公理。注意我们这么做的唯一理由是尽可能使得讨论所用语义的一致性和精确性。我们假定欧阳耿在其文章摘要中提到的“传统的有穷-无穷”理论体系指的就是我们约定的数学的数学分析部分。其中常用的数学概念按长期流行的方式定义(不合生成规则的概念本文将加以严格化。即给出合乎法则的定义)。如果欧阳耿所说的理论体系不是如此，他列举的‘悖论’不属于我们理解的数学，那么不管他的文章说了什么，连同他的“永远不可能解决”
我们都会认为无关痛痒，

1. 无穷小，无穷大在数学分析里是具有某种度量拓扑性质的函数的俗称。
    我们说函数 f 在某数  a 的右邻域内是无穷小，是指 &#8704;ε>0 &#8707;δ>0 ((0<x - a<δ) &#8658; |f(x)| < ε)
       即对任意差距 ε (>0), 存在相应的差距 δ (>0)，只要 x 比 a 大而且两者的差距小于 δ，
       函数 f 在 x 的值与 0 的差距就小于 ε.  这个性质的等价表达是  f(x)→0 (x→a+).
       另一个说法是 f 关于 a 的右极限是 0.  更古老更形象也是更有误导性的说法是： 当 x 从右边
       趋于 a 时 f(x) 趋于 0， 或者说 f(x) 是 x 从右边趋于 a 时的无穷小量。

    我们说函数 f 在某数  a 的右邻域内是无穷大，是指 &#8704;N>0 &#8707;δ>0 ((0<x - a<δ) &#8658; |f(x)| > N)
       f 的这个性质俗称： f(x) 是 x 从右边趋于 a 时的无穷大量。

   我们说函数 f 在-∞的邻域内是无穷大，是指 &#8704;N>0 &#8707;M>0 ((x < -M) &#8658; |f(x)| > N)
       f 的这个性质俗称： f(x) 是 x 趋于负无穷时的无穷大量。

   类似地容易知道其他无穷小，无穷大的确切定义。

   可见无穷大，无穷小是具有某种极限（局部，但不是单点）性质的函数，我们问 π
   有多大是指找出它的某种程度的数值估算或者它在数轴上的近似位置，多大多小的问题只对
   特定的量有意义。问具有极限性质的函数到底多大多小没有意义。

2. 数学不涉及时间。
   张三李四解同一个方程花的时间不同，但方程的解是方程本身的性质，跟时间无关。
   极限是某些函数的性质，个人求极限需要时间，取极限理论上不涉及时间。

3. 芝诺‘悖论’a (运动不存在)构造部分的数学等价表达是序列 {1/2^n} 有无穷多项，或者干脆说
    f：N → (0, 1] (f(n) = 1/2^n) 是单射. 更一般地，无非是说任一非蜕化线段上有无穷多个点。
   这件事跟运动有关系吗? 没有！这件事只跟芝诺想在跑道上标识无穷多个点有关系，芝诺把
   标识无穷多个点实践上的不可能（需要无穷长的时间）归结为运动不可能（绝妙的偷换概念）。
   芝诺标识跑道的那些对分点对运动本身没有任何必要。

4. 芝诺’悖论‘b (阿基里斯追不上乌龟) 这个佯谬的’永远‘也是偷换概念：本质上就是芝诺预设了
   一个规则，这个规则确定了阿基里斯尚未追上乌龟的时间段上的无穷多个记载点，后一个点
   是阿基里斯到达乌龟当下所在点时乌龟逃至的位置。芝诺把这种点的枚举的无穷性等同于
   阿基里斯未追上乌龟的时间段长度，颇具催眠效果。

5. 对芝诺构造’悖论‘的动机的揣摩最多不过是揣摩。但是芝诺’悖论‘给历代思想者的教益是巨大的。
   我们知道自然语言的多义性是’悖论‘的温床，有限事物内部的某种无限性常常可以用来构造‘悖论’，
   语义分析有助于破解‘悖论’。精确的定义可以避免‘悖论’。真正的悖论需要通过公理系统的修正
   才能避免（希望以后有机会回到这点来）。最后，芝诺‘悖论’对没有经过慎密思考和逻辑训练的
   后人，还会是悖论。但这不等于说芝诺‘悖论’至今没有被人类所彻底破解。

对欧阳耿的文章的一部分内容作了整理和评注。对下一贴将进入文章的极度混乱的部分也作
了一些理论准备。过年不比平常，可能要两天后才能贴出要说的话。

学生们11

elim，我昨天下午去导师那里，谈起在这里的经历，导师有点好奇，我让他看了这里面的内容，他看了之后一直摇头，特别是看了你和一个叫做jzkyllcjl的一些讨论后，说怎么骂来骂去简直不可思议，“不是学术讨论而是火药、战场”。叫我好好准备开学，不得浪费时间、介入这种是非。其实尽管没有在学术上得到什么，至少我也开了眼界、见识了另一种“学术讨论”。 elim，我不想再来了。

elim

听说那是欧阳耿的马甲。  http://tieba.baidu.com/p/3591329499。
不可全信，也不可不信。那地方“学生们11”又叫“小羊羔们”，这个叫法传神。

在职学术骗子不比 jzkyllcjl, 被双规损失是大了点。国内外学界把学痞凉在一边，
不甘寂寞来这里，不懂什么叫天网恢恢疏而不漏啊。

门外汉

来这里的大多数人，本来也是无所事事，那也就谈不上什么浪费时间一说了。

elim

无所事事的把这里当回事，就有所事事了，在别处有所事事的也许到这里是浪费时间，也许也能在这里有所事事。

elim