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Author: Noam Greenberg
Publisher: Cambridge University Press
ISBN: 110751200X
Category : Mathematics
Languages : en
Pages : 205
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Book Description
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.
Author: Noam Greenberg
Publisher: Cambridge University Press
ISBN: 110751200X
Category : Mathematics
Languages : en
Pages : 205
Get Book Here
Book Description
Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.
Author: Alessandro Andretta
Publisher: American Mathematical Society
ISBN: 1470452731
Category : Mathematics
Languages : en
Pages : 189
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Book Description
View the abstract.
Author: Zubaidah
Publisher: Azwar Rangkuti
ISBN:
Category : Education
Languages : en
Pages : 49
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Book Description
This research entitled “Teaching countable noun and uncountable noun to the first year students of MTsS Terpadu Langsa.” It is aimed to know how the teaching process in teaching countable noun and uncountable noun in that school. The writer used two research methods in getting data to the research. They are library research and field research.
Author: Thomas J. Jech
Publisher: American Mathematical Soc.
ISBN: 0821822144
Category : Mathematics
Languages : en
Pages : 77
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Book Description
This work is a systematic study of ideals over uncountable sets. In particular, we investigate the role of various properties of ideals in arithmetic of cardinal numbers. We also study consequences of existence of precipitous ideals for the generalized continuum hypothesis and the singular cardinals problem.
Author: Raul Moncayo
Publisher: Routledge
ISBN: 0429907761
Category : Psychology
Languages : en
Pages : 237
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Book Description
Lacan critiqued imaginary intuition for confusing direct perception with unconscious pre-conceptions about people and the world. The emphasis on description goes hand in hand with a rejection of theory and the science of the unconscious and a belief in the naive self-transparency of the world. At the same time, knowing in and of the Real requires a place beyond thinking, multi-valued forms of logic, mathematical equations, and different conceptions of causality, acausality, and chance. This book explores some of the mathematical problems raised by Lacan's use of numbers and the interconnection between mathematics and psychoanalytic ideas. Within any system, mathematical or otherwise, there are holes, or acausal cores and remainders of indecidability. It is this senseless point of non-knowledge that makes change, and the emergence of the new, possible within a system. This book differentiates between two types of void, and aligns them with the Lacanian concepts of a true and a false hole and the psychoanalytic theory of primary repression.
Author:
Publisher:
ISBN:
Category : Communicable diseases
Languages : en
Pages : 688
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Book Description
Author: David Nirenberg
Publisher: University of Chicago Press
ISBN: 022664698X
Category : History
Languages : en
Pages : 429
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Book Description
"From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--
Author: Jack C. Richards
Publisher: Cambridge University Press
ISBN: 9780521449359
Category : Foreign Language Study
Languages : en
Pages : 164
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Book Description
Changes is a three-level general English course for adult and young adult learners. Changes ensures that students have every opportunity to develop confident communicative ability as well as accuracy in English.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 762
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Book Description
Author: David Nirenberg
Publisher: University of Chicago Press
ISBN: 0226828360
Category : History
Languages : en
Pages : 429
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Book Description
Ranging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity. Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity? These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schrödinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.
