Kybernetes: Volume 37 Issue 3/4
Strapline:
The international journal of cybernetics, systems and management sciencesTable of contents - Special Issue: Systematic Studies: The Infinity Problem in Modern Mathematics
Guest Editors: Yi Lin
Systemic yoyo structure in human thoughts and the fourth crisis in mathematics
Yi Lin, Wujia Zhu, Ningsheng Gong, Guoping DuThe paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the…
Descriptive definitions of potential and actual infinities
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper's purpose is to analyze the concepts of potential and actual infinities.
Wide‐range co‐existence of potential and actual infinities in modern mathematics
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper aims to introduce the concepts of potential and actual infinities.
Modern system of mathematics and a pair of hidden contradictions in its foundation
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper's aim is to show a pair of deeply hidden contradictions in the system of mathematics.
The inconsistency of countable infinite sets
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThe paper aims to show countable infinite sets are self‐contradictory non‐sets.
Inconsistency of uncountable infinite sets under ZFC framework
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThe purpose is to show that all uncountable infinite sets are self‐contradictory non‐sets.
Modern system of mathematics and special Cauchy theater in its theoretical foundation
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThe paper aims to employ a different approach to show that the countable infinite sets are self‐contradictory non‐sets.
Modern system of mathematics and general Cauchy theater in its theoretical foundation
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThe paper aims to show using a different method that any uncountable set is a self‐contradictory non‐set.
Cauchy theater phenomenon in diagonal method and test principle of finite positional differences
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper's purpose is to show a class of well‐used methods in set theory is invalid.
New Berkeley paradox in the theory of limits
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper's aim is to reveal the return of the Berkeley paradox of the eighteenth century.
The inconsistency of the natural number system
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThe paper aims to use a third method to show that the system of natural numbers is inconsistent.
Mathematical system of potential infinities (I) – preparation
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongAims to focus on the co‐existence of potential and actual infinities in modern mathematics and its theoretical foundation. It has been shown that not only the whole system of…
Mathematical system of potential infinities (II) – formal systems of logical basis
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThis is the second part of the effort to resolve the following two problems that badly need an answer: how can an appropriate theoretical foundation be chosen for modern…
Mathematical system of potential infinities (III) – meta theory of logical basis
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThis paper is the third part of the effort to resolve the following two problems, which urgently need an answer: how can an appropriate theoretical foundation be chosen for modern…
Mathematical system of potential infinities (IV) – set theoretic foundation
Wujia Zhu, Yi Lin, Guoping Du, Ningsheng GongThis paper is the fourth part of the effort to resolve the following two problems that urgently need an answer: how can an appropriate theoretical foundation be chosen for modern…
Problem of infinity between predicates and infinite sets
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuThe paper's aim is to reconsider the feasibility at both the heights of mathematics and philosophy of the statement that each predicate determines a unique set.
Intension and structure of actually infinite, rigid sets
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping DuOn the basis of previous work, the authors aim to further study the problem of infinity existing in between predicates and sets.
The challenges of tracking and protecting data
B.H. Rudall, C.J.H. MannThis paper aims to review current research and developments with particular reference to some of the challenges of tracking and protecting data when innovative methods of capture…
Dealing with spam: more on climate change
Alex M. AndrewAims to focus on aspects of the menace of spam, or unsolicited messages by e‐mail, are treated, especially a service designed to stop spam at or near its source. A TV documentary…
