New Berkeley paradox in the theory of limits

被引：8

作者：

Zhu, Wujia ^{[2
]}

Lin, Yi ^{[1
]}

Gong, Ningsheng ^{[3
]}

Du, Guoping ^{[4
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Coll Econ & Management, Nanjing 210016, Peoples R China

[2] Slippery Rock Univ, Dept Math, Slippery Rock, PA 16057 USA

[3] Nanjing Univ Technol, Coll Informat Sci, Nanjing 210009, Peoples R China

[4] Nanjing Univ, Inst Modern Log & Applicat, Nanjing 210008, Peoples R China

来源：

KYBERNETES | 2008年 / 37卷 / 3-4期

关键词：

cybernetics; set theory; mathematics;

D O I：

10.1108/03684920810863453

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Purpose - The paper's aim is to reveal the return of the Berkeley paradox of the eighteenth century. Design/methodology/approach - This is a conceptual discussion. Findings - Since, long time ago, the common belief has been that the establishment and development of the theory of limits had provided an explanation for the Berkeley paradox. However, when the authors revisit some of the age-old problems using the thinking logic of allowing both the concepts of potential and actual infinities, they find surprisingly that the shadow of the Berkeley paradox does not truly disappear in the foundation of mathematical analysis. Originality/value - Show the incompleteness of the theory of limits, which is not the same as what has been believed in the history of mathematics.

引用

页码：474 / 481

页数：8

共 10 条

[1] KLINE M, 1979, MATH THOUGHTS ANCIEN, V1
[2] Systemic yoyo structure in human thoughts and the fourth crisis in mathematics
Lin, Yi
Zhu, Wujia
Gong, Ningsheng
Du, Guoping
[J]. KYBERNETES, 2008, 37 (3-4) : 387 - 423
[3] Modern system of mathematics and special Cauchy theater in its theoretical foundation
Zhu, Wujia
Lin, Yi
Du, Guoping
Gong, Ningsheng
[J]. KYBERNETES, 2008, 37 (3-4) : 458 - 464
[4] Cauchy theater phenomenon in diagonal method and test principle of finite positional differences
Zhu, Wujia
Lin, Yi
Gong, Ningsheng
Du, Guoping
[J]. KYBERNETES, 2008, 37 (3-4) : 469 - 473
[5] Modern system of mathematics and general Cauchy theater in its theoretical foundation
Zhu, Wujia
Lin, Yi
Du, Guoping
Gong, Ningsheng
[J]. KYBERNETES, 2008, 37 (3-4) : 465 - 468
[6] The inconsistency of countable infinite sets
Zhu, Wujia
Lin, Yi
Du, Guoping
Gong, Ningsheng
[J]. KYBERNETES, 2008, 37 (3-4) : 446 - 452
[7] Inconsistency of uncountable infinite sets under ZFC framework
Zhu, Wujia
Lin, Yi
Du, Guoping
Gong, Ningsheng
[J]. KYBERNETES, 2008, 37 (3-4) : 453 - 457
[8] Descriptive definitions of potential and actual infinities
Zhu, Wujia
Lin, Yi
Gong, Ningsheng
Du, Guoping
[J]. KYBERNETES, 2008, 37 (3-4) : 424 - 432
[9] Modem system of mathematics and a pair of hidden contradictions in its foundation
Zhu, Wujia
Lin, Yi
Gong, Ningsheng
Du, Guoping
[J]. KYBERNETES, 2008, 37 (3-4) : 438 - 445
[10] Wide-range co-existence of potential and actual infinities in modern mathematics
Zhu, Wujia
Lin, Yi
Gong, Ningsheng
Du, Guoping
[J]. KYBERNETES, 2008, 37 (3-4) : 433 - 437

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