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Proofs : a long-form mathematics textbook
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ISBN: 9798595265973 Year: 2021 Publisher: [Sacramento, CA] : [LongFormMath.com],

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This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor. This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory. After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics. In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice.

Keywords

Proof theory


Book
Y a-t-il un Dieu ?
Authors: ---
ISBN: 9782916120096 2916120092 Year: 2009 Publisher: Paris : Ithaque,

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Pour R. Swinburne, spécialiste anglais de philosophie de la religion chrétienne et du théisme, l'existence de Dieu permet d'expliquer des données que les sciences de la nature n'expliquent pas, comme l'existence de l'Univers et de ses lois. Elle est aussi l'hypothèse métaphysique la plus simple pour en rendre compte, et qui a, a priori pour elle, la probabilité la plus grande.

Keywords

God --- Dieu --- Proof --- Existence


Book
Dieu existe : arguments philosophiques.
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ISBN: 9782204099042 220409904X Year: 2013 Publisher: Paris Cerf

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La question philosophique de l'existence de Dieu.
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ISBN: 2130461247 9782130461241 Year: 2010 Publisher: Paris PUF

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Book
La probabilité du théisme
Authors: ---
ISSN: 16242459 ISBN: 9782711626113 2711626113 Year: 2015 Publisher: Paris : Vrin,

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Le philosophe s'interroge sur la cohérence et la complexité du théisme et expérimente son pouvoir prédictif. Il souhaite éprouver l'hypothèse métaphysique de l'existence de Dieu et étaye son propos avec les théories de Thomas d'Aquin, Duns Scot, Isaac Newton, etc. ©Electre 2016

Keywords

God --- Theism --- Dieu --- Théisme --- Proof --- Existence --- Théisme --- Existence. --- Théisme. --- God - Proof


Book
Rethinking Anselm's arguments
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ISBN: 9789004358263 9789004363663 9004358269 9004363661 Year: 2018 Volume: 1 Publisher: Leiden Boston

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"This book re-examines Anselm's famous arguments for the existence of God in his Proslogion, and in his Reply. It demonstrates how he validly deduces from plausible premises that God so truly exists that He could not be thought not to exist. Most commentators, ancient and modern, wrongly located his argument in a passage which is not about God at all. It becomes evident that, consequently, much contemporary criticism is based on misreading and misunderstanding his text. It reconstructs his reasoning through three distinct but logically connected stages. It shows that, even if Anselm's crucial premises are sceptically interpreted, his conclusions still follow. Properly understood, this argument is not vulnerable to the standard criticisms, including Gaunilo's 'Lost island' counter-example"--


Book
Traité de l'existence de Dieu
Authors: ---
ISBN: 2711304175 9782711304172 Year: 1990 Volume: vol *6 Publisher: Bruxelles: Éditions universitaires,

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L'esprit de l'athéisme et son destin
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ISBN: 2710326159 9782710326151 Year: 2003 Volume: 206 Publisher: Paris : Table ronde,

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Le débat philosophique sur l'athéisme semble aujourd'hui passé de mode. Il est vrai que l'affrontement entre le théisme et l'antithéisme, qui a longtemps nourri la figure de l'athéisme classique, paraît avoir été emporté avec l'écume de l'histoire, du moins dans certaines parties de notre Occident. Mais en cessant de poser problème, l'athéisme est-il devenu pour autant solution ? De toute façon, c'est aller trop vite en besogne que de tenir pour nulle et périmée la question de l'affirmation ou de la négation de Dieu. A condition de tirer au clair, autant crue faire se peut, la question de l'identité de ce Dieu. A condition, surtout, de remarquer que l'athéisme ne se réduit pas à la négation de l'existence de Dieu, hors de tout contexte. Ce qui nous plonge dans un embarras croissant, tant l'athéisme semble alors se diluer dans ses formes variées, au point de devenir insaisissable. Il peut être philosophique ou existentiel, s'exposer bruyamment ou se lover dans le silence, s'exprimer dans l'angoisse comme dans l'insouciance, prendre le visage de la barbarie comme celui de la culture. C'est finalement comme expression d'une logique à l'œuvre, opposée point par point à celle du christianisme, mais toujours en relation étroite avec elle, que l'athéisme se donne à penser.

Keywords

Atheism. --- God --- Athéisme --- Dieu --- Proof --- Existence --- Athéisme

Proof theory
Authors: ---
ISBN: 3540079114 0387079114 364266475X 3642664733 9783540079118 Year: 1977 Volume: 225 Publisher: Berlin: Springer,

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How to read and do proofs : an introduction to mathematical thought processes
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ISBN: 0471680583 9780471680581 Year: 2005 Publisher: Hoboken, NJ [u.a.] Wiley

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