Infinite Value

This unusually clear and interesting classic offers a thorough and reliable treatment of an important branch of higher analysis. The work covers real numbers and sequences, foundations of the theory of infinite series, and development of the theory (series of valuable terms, Euler's summation formula, asymptotic expansions, and other topics). Exercises throughout. Ideal for self-study.

People tend to rank values of all kinds linearly from good to bad, but there is little reason to think that this is reasonable or correct. This book argues, to the contrary, that values are often partially ordered and hence frequently incomparable. Proceeding logically from a small set of axioms, John Nolt examines the great variety of partially ordered value structures, exposing fallacies that arise from overlooking them. He reveals various ways in which incomparability is obscured: using linear indices to summarize partially ordered data, relying on an inadequately defined concept of parity, or conflating incomparability with vagueness. Incomparability can enrich and clarify a range of topics including the paradoxes of Derek Parfit, rational decision theory, and the infinite values of theology. Finally, Nolt shows how to generalize many of the concepts introduced earlier, explores the intricate depths of certain noteworthy partially ordered value structures, and argues for the finitude of value. Incomparable Values will be of interest to scholars and advanced students working in ethics, value theory, rational decision theory, and logic.

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite. This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields. The volume is divided into four parts. Part I reviews the first decade of SIP (1962-1972). Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming. New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III. Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

After repeated beatings, which started when I was in Kindergarten, I learned two certainties in life: I was worthless and I was unlovable. These beliefs permeated every aspect of my life from my family, to the classroom, and on to the basketball court. It followed me beyond school into my professional life, and even my new family, I became BLIND to the value that was in me, and the value that I could truly add to the world around me. Jim Rohn said, "It is more important to work harder on yourself, than you do on your job." IV4S reveals my journey as I worked to shine a light through the blindness of my value both inside and out of the classroom. The journey has uncovered one of the greatest truths the world has ever known. First and foremost, I am INFINITELY VALUABLE. The second discovery is the fact that there is an INFINITE amount of VALUE that I can add to the world around me. As a student and professional, I believed that my value was conditional. If I did well on a test, my value increased by 1 point. But if I had a bad basketball game, it decreased by 1,378 points. In a professional setting, you are only as good as your last sale or accomplishment. Fortunately, my journey revealed the reality that my value isn't conditional or static, but it is accumulating. As humans, we are the summation of all of our life experiences. It is that ever increasing minute by minute, second by second total that ultimately calculates your True Market Value. Once I was able to correctly calculate my Inherent Value, I was then able to more clearly decide what type of value that I would like to add to the marketplace and society. During my blindness, I could only see the value that I could add to someone else's company, through telling their story. The journey you are about to read is the First revelation of the Infinite amount of Value that I will add to the marketplace through telling my story and sharing my talents. When you choose to read this book in its entirety, I promise you that you will have a mirror to see both your Inherent Value and the Value that you will be able to add to the world around you. (Spoiler Alert: They are Both INFINITE!). You will be provided with tools and resources that I didn't have when I was a kid and student that will aid you uncovering your True Value even sooner. (It took me over 30 years). I could tell you to read this book to benefit yourself, but that would be too finite. You should read this book for the thousands upon thousands of people that your life will add Value to once you do. Another important reality that I learned on this journey is "It's not ONLY about me!" If it was only about me, then the tough times that I went through would really suck (not that it didn't hurt at the time, because it did). There are lives that I will be able to add value to, because I went through my beatings. And that is why I write. There are thousands of lives around this planet right now that are waiting to be helped by your experiences. My journey can show you a path to be able to reach the people you are supposed to add your INFINITE VALUE to.

“The present volume is the first in a projected trilogy, the other two of which are ‘On the Logical Demonstration of Divine Existence’ and ‘On the Logical Origins of Right’. The entire work could be described as an essay concerning the ontological basis of political philosophy. “What an elementary work on the logic of infinitary sets can possibly have to do with political philosophy will become apparent only as the various arguments unfold. The connection is reasonably straightforward, however, and has to do with the relation of what I call ‘analytic impressionism’ to the general rationale of revolution: it is to regard a contradictory, anomalous, or even immoral situation—a fantasia of some kind—as a done thing and then cook up a story about how, notwithstanding, it might have been accomplished or justified rationally. The goal of all this is to be able to do with a certain impunity whatever you can contrive to get away with, and in particular to appropriate the primacy of right for oneself: all of which is rooted in the desiccated ontology of virtualization and results in a narcissistic and infantilized culture.” From the Preface

This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature — this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in. Contents: The Three Parts of EverythingSources of RandomnessRandomness in the UniverseThe Emergence of Real WorldThe Role of Randomness Readership: Academic and general public. Keywords:Randomness;Chaos;Fractals;Determinism;Natural ProcessesKey Features:Differs from other books on this subject in that it treats randomness from a complex systems point of view rather than from a solely probabilistic oneSuitable for the general public with an interest in scienceUseful for scientists in all areasReviews:“Reading the book is like visiting a museum, and as the reader goes successively through the chapters he (or she) encounters beautiful ideas and interesting comments. Although the book is not a book on the history of mathematics, it contains interesting historical facts.”Zentralblatt MATH “I recommend reading it to those who want a quick introduction to ideas about randomness and those whose exposure to these ideas has been piecemeal, as mine was. The book may spark the imaginations of readers and advance our science through innovative application of the concepts. Someone might just find life-changing inspiration.”Vadose Zone Journal “As a contribution to popular science this book is welcome. Tsonis explains randomness as it enters into mathematics, science and everyday life.”Mathematical Reviews