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Author: Nathaniel S. Hellerstein
Publisher: World Scientific
ISBN: 9789812796110
Category : Mathematics
Languages : en
Pages : 274
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Book Description
This book is about OC diamondOCO, a logic of paradox. In diamond, a statement can be true yet false; an OC imaginaryOCO state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, GAdelian meta-mathematics and dilemma games."
Author: Nathaniel S. Hellerstein
Publisher: World Scientific
ISBN: 9789812796110
Category : Mathematics
Languages : en
Pages : 274
Get Book Here
Book Description
This book is about OC diamondOCO, a logic of paradox. In diamond, a statement can be true yet false; an OC imaginaryOCO state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, GAdelian meta-mathematics and dilemma games."
Author: N. S. Hellerstein
Publisher: World Scientific
ISBN: 9814287148
Category : Mathematics
Languages : en
Pages : 311
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Book Description
This book is about ''diamond'', a logic of paradox. In diamond, a statement can be true yet false; an ''imaginary'' state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer-Brown modulator; and Metamathematical Dilemma, which relates diamond to Godelian meta-mathematics and dilemma games.
Author: Nathaniel S Hellerstein
Publisher: World Scientific
ISBN: 9814466832
Category : Mathematics
Languages : en
Pages : 311
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Book Description
This book is about “diamond”, a logic of paradox. In diamond, a statement can be true yet false; an “imaginary” state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued Boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer-Brown “modulator”; and Metamathematical Dilemma, which relates diamond to Gödelian metamathematics and dilemma games.
Author: Nathaniel S Hellerstein
Publisher: World Scientific
ISBN: 9814498262
Category : Mathematics
Languages : en
Pages : 271
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Book Description
This book is about “diamond”, a logic of paradox. In diamond, a statement can be true yet false; an “imaginary” state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, Gödelian meta-mathematics and dilemma games.
Author: Nathaniel S Hellerstein
Publisher: World Scientific
ISBN: 9814497037
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This book is about “delta”, a paradox logic. In delta, a statement can be true yet false; an intermediate state, midway between being and non-being. Delta's imaginary value solves many paradoxes unsolvable in two-valued Boolean logic, including Russell's, Cantor's, Berry's and Zeno's.Delta has three parts: “inner delta logic”, covering “Kleenean logic”, which resolves self-reference; outer delta logic, covering Z mod 3, conjugate logics, cyclic distribution, and the voter's paradox; and “beyond delta logic”, covering four-valued logic and games.
Author: Nathaniel Hellerstein
Publisher: World Scientific
ISBN: 9810232438
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This book is about "delta", a paradox logic. In delta, a statement can be true yet false; it is an "imaginary" state, midway between being and non-being. Delta's imaginary value solves many logical dilemmas unsolvable in two-valued Boolean logic. Delta resolves these paradoxes -- Russell's, Cantor's, Betty's and Zeno's. Delta has two parts: inner delta logic, or "Kleenean logic", which resolves the classic paradoxes of mathematical logic; and outer delta logic, which relates delta to Z mod 3, conjugate logics, cyclic distribution, and the voter' paradox.
Author: Nathaniel Shawn Hellerstein
Publisher:
ISBN:
Category :
Languages : en
Pages : 248
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Book Description
Author: Jorge Alberto Calvo
Publisher: World Scientific
ISBN: 9812561870
Category : Mathematics
Languages : en
Pages : 640
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Book Description
The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year.This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Author: Yongju Bae
Publisher: World Scientific
ISBN: 9811292779
Category : Mathematics
Languages : en
Pages : 456
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Book Description
This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Author: David N Yetter
Publisher: World Scientific
ISBN: 9814492248
Category : Mathematics
Languages : en
Pages : 238
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Book Description
Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
