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The word 'infinity' usually elicits feelings of awe, wonder, and admiration; the concept infinity has fascinated philosophers and theologians. The author shows how professional mathematicians tame this unwieldy concept, come to terms with it, and use its various aspects as their most powerful tools of the trade. The early chapters are descriptive and intuitive, full of examples that not only illustrate some infinite processes, but that are worth studying for their own sake. Many questions are raised in the beginning, partially answered in various contexts throughout the book, and finally treated with the precision necessary to give the reader an excellent grasp of the fundamental notions used in the calculus as well as in virtually all other mathematical disciplines. The text is peppered with challenging problems whose solutions appear at the end of the book.

Processes, Infinite. --- Infinite.

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"A bold and all-embracing exploration of the nature and progress of knowledge from one of today's great thinkers. Throughout history, mankind has struggled to understand life's mysteries, from the mundane to the seemingly miraculous. In this important new book, David Deutsch, an award-winning pioneer in the field of quantum computation, argues that explanations have a fundamental place in the universe. They have unlimited scope and power to cause change, and the quest to improve them is the basic regulating principle not only of science but of all successful human endeavor. This stream of ever improving explanations has infinite reach, according to Deutsch: we are subject only to the laws of physics, and they impose no upper boundary to what we can eventually understand, control, and achieve. In his previous book, The Fabric of Reality, Deutsch describes the four deepest strands of existing knowledge-the theories of evolution, quantum physics, knowledge, and computation-arguing jointly they reveal a unified fabric of reality. In this new book, he applies that worldview to a wide range of issues and unsolved problems, from creativity and free will to the origin and future of the human species. Filled with startling new conclusions about human choice, optimism, scientific explanation, and the evolution of culture, The Beginning of Infinity is a groundbreaking book that will become a classic of its kind"--

Explanation --- Infinite --- Science --- Philosophy

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L'Idee de l'Infini a ete decouverte par Descartes dans les Meditations Metaphysiques. Il restait apres Descartes a elucider la signification de cette Idee eminente par la concretisation de son contenu. L'experience vecue qui articule concretement le developpement de l'Idee de l'Infini est la socialite. En elle, la presence de l'etre transcende l'horizon limitatif de la decouverte intellective de la comprehension ou constitution de l'etre a partir de sa mise en lumiere. L'Idee de l'Infini revele ainsi une face nocturne des evenements de l'etre echappant a l'ontologie qui gouverne la philosophie occidentale. Le debordement de l'etre sur l'ontologie coincide sans reste avec l'ethique. Lui seul permet d'annoncer la venue dans l'etre de la paix messianique par-dela l'ontologie de la guerre et les illusions de la morale. Suivant Levinas en son chef-d'oeuvre de 1961, Totalite et Infini, nous interrogeons dans ce livre le sens d'une telle presence eminente de l'etre en ses evenements ultimes essentiellement nocturnes. Nous cherchons a montrer pourquoi la sensibilite, la socialite, l'eros et la fecondite representent autant d'experiences paroxystiques de l'etre dont la production echappe par principe a la lumiere de l'ontologie. C'est a l'elucidation de tels evenements clandestins que se consacre le present essai.

Whole and parts (Philosophy) --- Infinite. --- Phenomenology. --- Lévinas, Emmanuel.

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« L’Époque dénouée » s’attache à démêler les fils embrouillés de la Tradition afin de comprendre ce qui nous arrive, à nous les tard venus. À cette fin, Gérard Granel s’engage dans une analyse historico-historiale visant à déterminer la « loi la plus intime » de notre monde. Le nœud thématique qu’il retient dans les textes réunis dans ce volume est celui de l’« automate » dont il montre qu’il possède un triple nouage historique : la substantification par Platon de la psychè auto-mate, qui dessine la figure de la pensée comme mathesis ; l’universalisation par Descartes de l’idée de mathesis, dont le moteur est une logique de l’infinité induisant un devenir-ingénieur de l’esprit et une détermination du savoir comme savoir « automate » ; la propagation, mise en évidence par Marx, du principe d’infinité à tous les domaines d’activité, qui transforme le monde lui-même en une vaste « accumulation de marchandises » ne connaissant d’autre loi que celle imposée par la « substance automatique ». Démêler le nœud de l’automate fait donc lever la question suivante, qui fut celle de Nietzsche avant de devenir celle de Heidegger, et qui est aussi celle à laquelle nous confronte le versant non métaphysique des analyses de Marx : comment nous départir de notre appartenance à un monde qui semble périmer tout avenir ?

Civilization, Modern. --- Infinite --- Philosophy, Modern --- Civilisation moderne et contemporaine --- Infini --- Philosophie moderne

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This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.

Inequalities (Mathematics). --- Inequalities (Mathematics) --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Algebra --- Processes, Infinite. --- Infinite processes --- Mathematics. --- Algebra. --- Popular works. --- Popular Science, general. --- Mathematics Education. --- Study and teaching. --- Continued fractions --- Products, Infinite --- Series --- Processes, Infinite --- Science (General). --- Math --- Science --- Mathematical analysis --- Mathematics—Study and teaching .