汉语是联合国官方正式使用的6种同等有效语言之一。请不要歧视汉语！

Chinese is one of the six equally effective official languages of the United Nations.

Not to discriminate against Chinese, please!

平等的相对性与欺骗性（P 对 NP，P vs NP）

与（科学网博主谁比谁强多少又差多少？）：

卡片机傻拍2016（132）

佳能卡片机SX170 IS试拍。感谢您的指教！只压缩，未做其它调整。

    在我们的世界上，“不平等”大概是主流现象。我们很难找到平等：湖水、沙漠等，在很小的范围，的确可以“平”。但大范围，却是惊涛骇浪、跌宕起伏。

（1）拍摄于 2016-08-20 13:07 许，卫津路老校区第14教学楼前的苹果园。

“高斯苹果树”同一枝头上结出的4枚苹果：

一枚“被”早早夭折成木乃伊；另一枚“被”瘦小；最大的那枚苹果，也最风采圆润。

（2）拍摄于 2016-08-17 11:43 许，卫津路绿化带。

    忘记 ZFC 里的“幂集公理（Axiom of power set）”以及由此信念证明的“康托定理（ Cantor theorem ）”，使得“P vs NP”的研究，走了多大的弯路。都是丘奇-图灵论题（Church–Turing thesis）给误导的。

ZFC（或“康托定理”），还是“丘奇-图灵论题”，哪个更可信？

下图把颜色加黑：

相关链接：

[1] 李俊，2016-09-25 ，科学网博主谁比谁强多少又差多少？

http://blog.sciencenet.cn/blog-5800-1005001.html

[2] 柳渝，2016-08-30，NP理论（3）：层次与中国传统逻辑

http://blog.sciencenet.cn/blog-2322490-999674.html

[3] 柳渝，2016-05-24，NP理论（1）：图灵机与丘奇－图灵论题  精选

http://blog.sciencenet.cn/blog-2322490-979317.html

[4] Church–Turing thesis - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis

      It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource limitations, if and only if it is computable by a Turing machine.

[5] History of the Church–Turing thesis - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/History_of_the_Church%E2%80%93Turing_thesis

[6] The Church-Turing Thesis - Stanford Encyclopedia of Philosophy

http://plato.stanford.edu/entries/church-turing/

[7] Church-Turing Thesis -- from Wolfram MathWorld

http://mathworld.wolfram.com/Church-TuringThesis.html

     The Church-Turing thesis (formerly commonly known simply as Church's thesis) says that any real-world computation can be translated into an equivalent computation involving a Turing machine

[8] Church thesis - Encyclopedia of Mathematics

https://www.encyclopediaofmath.org/index.php/Church_thesis

http://www.encyclopediaofmath.org/index.php?title=Church_thesis&oldid=35574

     A principle according to which the class of functions computable by means of algorithms in the broad intuitive sense (cf. Algorithm), coincides with the class of partial recursive functions. Church' thesis is this fact of nature, which is confirmed by the experience accumulated in mathematics throughout its history.

[9] Church's thesis | mathematics | Britannica.com

https://global.britannica.com/topic/Churchs-thesis

     Church’s thesis, also called Church’s Theorem, a principle formulated by the 20th-century American logician Alonzo Church, stating that the recursive functions are the only functions that can be mechanically calculated.

[10] ZFC, Zermelo–Fraenkel set theory with the axiom of choice. Akihiro Kanamori (originator), Encyclopedia of Mathematics.

https://www.encyclopediaofmath.org/index.php/ZFC

http://www.encyclopediaofmath.org/index.php?title=ZFC&oldid=19298

       A5) Axiom of power set:

      This axiom asserts, for any set x, the existence of its power set, the set consisting exactly of those sets v that are subsets of x.

[11] Cantor theorem - Encyclopedia of Mathematics.

https://www.encyclopediaofmath.org/index.php/Cantor_theorem

http://www.encyclopediaofmath.org/index.php?title=Cantor_theorem&oldid=37338

      The set 2^A of all subsets of a set A is not equipotent to A or to any subset of it.

[12]  Zermelo–Fraenkel set theory - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

[13] Zermelo-Fraenkel Set Theory -- from Wolfram MathWorld

http://mathworld.wolfram.com/Zermelo-FraenkelSetTheory.html

[14] Zermelo-Fraenkel Set Theory - Stanford Encyclopedia of Philosophy

http://plato.stanford.edu/entries/set-theory/ZF.html

[15] Cantor's theorem - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cantor%27s_theorem

[16] Cantor's theorem | mathematics | Britannica.com

https://global.britannica.com/topic/Cantors-theorem

      Cantor’s theorem, in set theory, the theorem that the cardinality (numerical size) of a set is strictly less than the cardinality of its power set, or collection of subsets. In symbols, a finite set S with n elements contains 2ⁿ subsets, so that the cardinality of the set S is n and its power set P(S) is 2ⁿ. While this is clear for finite sets,

[17] YANG Zhengling (杨正瓴). A non-canonical example to support that P is not equal to NP. Transactions of Tianjin University, 2011, 17(6): 446-449.

http://link.springer.com/article/10.1007%2Fs12209-011-1593-5

Ei Compendex, Accession number: 20120714762933

[18] “P对NP”难题研究的形转换新思路，中科院在线《科学智慧火花》，2011-08-30，

http://idea.cas.cn/viewdoc.action?docid=1275

[19] 杨正瓴，第二类计算机构想. 中国电子科学研究院学报, 2011, 6(4): 368-374.

Conception of the second class computer. Journal of China Academy of Electronics and Information Technology, 2011, 6(4): 368-374. (in Chinese)

http://mall.cnki.net/magazine/Article/KJPL201104010.htm

[20] 2012-03-23，[请教] P对NP：请郝克刚教授等专家指教（一）

http://blog.sciencenet.cn/blog-107667-550859.html

[21] 张永祥，2014-06-27，顶级科学大师丝语: 俄罗斯玩不玩CNS?  精选

http://blog.sciencenet.cn/blog-1076418-806951.html

http://blog.sciencenet.cn/blog-107667-987347.html

    俄罗斯数学传统的另一特点是倾向于全面地把数学看成一个充满活力的有机体。西方学界有可能一个人只是数学上某一方面的专家，而对相邻分支一无所知。一个学者涉猎较广在西方学界被看成一大缺点，而恰恰在俄罗斯一个学者研究领域太窄被看成同样程度的不足。

    推导的链（即所谓的“证明”）越长越复杂，最后得到的结论可靠性越低。复杂的模型几乎毫无用处。

感谢您的指教！

感谢您指正以上任何错误！