'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, IndependentIn our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely?In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility.'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman Read more

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. Read more

Infinity is a profoundly counter-intuitive and brain-twisting subject that has inspired some great thinkers – and provoked and shocked others. The ancient Greeks were so horrified by the implications of an endless number that they drowned the man who gave away the secret. And a German mathematician was driven mad by the repercussions of his discovery of transfinite numbers. Brian Clegg and Oliver Pugh's brilliant graphic tour of infinity features a cast of characters ranging from Archimedes and Pythagoras to al-Khwarizmi, Fibonacci, Galileo, Newton, Leibniz, Cantor, Venn, Gödel and Mandelbrot, and shows how infinity has challenged the finest minds of science and mathematics. Prepare to enter a world of paradox. Read more

Are you a slow reader? Is it difficult for you to memorise simple data in everyday life? Are you willing to make the most of your life by efficiently using your invaluable time?Then this book is a must read for you.The author of the present book unveils the secrets of excellence in the field of speed reading and memory mastery, which, in turn, helps us become a better version of ourself - a more confident, more efficient person in our evereaday life.This book is not a mere compilation of tricks and tips, rather, it is about the implementation of some ancient knowledge regarding the endless potentiality of human intellect.The present author focuses on 9 unheard and unique ways towards excellence in the field of of speed reading and memory mastery.Resources, now-a- days, are very much available to us; everyone knows about all the tricks and tips of every field - how to read faster, how to memorize data easily, how to stay focused etc.However, it's not really the knowledge but the implementation that makes the real difference. In spite of being a person with average IQ the present author now can read with a speed of 2000 wpm and can memorise 1000 digits at a stretch by practicing some of the ancient trics that almost everyone knows.It's a cliche that the brain is vaster than the sky; deeper than the sea.And, it's high time that we realise and maximise the power of our brain to its true potentiality.If you are looking for a Revolutionary way to increase your chances for personal and professional success and advancement, you must read this book.Focusing on the implementation of some unique ways, tried and tested personally, and few of the ancient trics and tips of memory mastery, this book becomes an absolutely practical and immensely beneficial piece of work. Read more

Sacred Geometry exists all around us in the natural world, from the unfurling of a rose bud to the pattern of a tortoise shell, the sub-atomic to the galactic. A pure expression of number and form, it is the language of creation and navigates the unseen dimensions beyond our three-dimensional reality.Since its discovery, humans have found many ways - stone circles, mandalas, labyrinths, temples- to call upon this universal law as a way of raising consciousness and communicating with a divine source. By becoming aware of the dots and lines that build the world around you, Sacred Geometry will teach you how to bring this mystical knowledge into your daily practice. Read more

What are the mysterious numbers that unlock the secrets of the universe?In Fantastic Numbers and Where to Find Them, leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics. These include Graham's number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite value could never be reached before the universe reset itself; and 10^{-120}, which measures the desperately unlikely balance of energy the universe needs to exist. . .Leading us down the rabbit hole to the inner workings of reality, Padilla demonstrates how these unusual numbers are the key to unlocking such mind-bending phenomena as black holes, entropy and the problem of the cosmological constant, which shows that our two best ways of understanding the universe contradict one another. Combining cutting-edge science with an entertaining cosmic quest, Fantastic Numbers and Where to Find Them is an electrifying, head-twisting guide to the most fundamental truths of the universe. Read more

PEN/WILSON LITERARY SCIENCE WRITING AWARD FINALIST 2023'A beautifully written meditation on mathematics: whimsical, thought-provoking and deep' ALEX BELLOS, author of Alex's Adventures in Numberland'Infinitely fascinating'THE TIMESOur universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing – no matter, no cosmos, not even empty space – could we create a universe using only maths?In this new mathematical origin story, mathematician and award-winning novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. With evocative and engaging examples ranging from multidimensional crochet to the Mona Lisa's asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence.Distilled from almost four decades of teaching experience, and offering both striking new perspectives for maths aficionados and an accessible introduction for enthusiastic novices, The Big Bang of Numbers proves that we can all fall in love with maths.'Who knew numbers could be so charming ... Suri takes us on a light-hearted journey all the way from nothing (zero) to infinity' KAREN JOY FOWLER, Booker-longlisted author of Booth Read more

Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books! Birds do it, bees do it, even educated fleas do it... Not falling in love, but counting. Animals and humans have been using numbers to navigate their way through the jungle of life ever since we all evolved on this planet. But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity...and beyond.On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity. Read more

Is anything truly random? Does infinity actually exist? Could we ever see into other dimensions? In this delightful journey of discovery, David Darling and extraordinary child prodigy Agnijo Banerjee draw connections between the cutting edge of modern maths and life as we understand it, delving into the strange – would we like alien music? – and venturing out on quests to consider the existence of free will and the fantastical future of quantum computers. Packed with puzzles and paradoxes, mind-bending concepts and surprising solutions, this is for anyone who wants life’s questions answered – even those you never thought to ask. Read more

From the author of Million Dollar Maths comes a fascinating and engaging look at the mathematics that lies behind our modern world. How does Google know what you want to type? How did humans first reach the moon? Could we ever have a supercomputer the size of a pinhead? In this thrilling numerical journey, Hugh Barker explores how mathematics has helped to build the technology of today, and the fascinating ways it is shaping the future. From green energy to 3-D printing and from quantum cryptography to machine learning, Quantum Leaps reveals the hidden mathematics in modern technology. Beautifully written and full of ingenious examples, this book will make you realise how the modern world would be impossible without our formidable mathematical armoury. Read more

This is a book about a number most of us know, the value of Pi = 3.14159... . It begins with someone scratching a circle in sand, then tells the nature and history of Pi and its endless digits, going out to the very edges of the Universe. For you who choose to join the author in memorizing digits of Pi, there are four choices, depending on whether you decide to fill the Observable Universe with yourself (learn 86 digits) to filling it with theoretical strings (191 digits). Join about 3,000,000,000,000,000,000,000,000,000,000 others in the Universe to know Pi, or perhaps more likely, its big brother Tau. All facts are documented, with pointers to sources for more information and speculation. Facts, history, science -- a great read -- all in good humor! Read more

This is For Visual Learner Folks™.Who Find Text-based Fractions No Fun :-)Do you wish to master maths Fractions Visually?In a few hours.UNDERSTANDING FRACTIONS VISUALLY In COLOUR is specifically designed to make learning fractions Visual, Fun & Easy To Follow.That's a solid promise, not a sales pitch to sell you something!Visual Fractions ChartsColour-coded charts from whole to halves, thirds, quarters, fifths, sixths, eighths, ninths, tenths and twelfthsHelps children visualise and understand fractions more easilyColour-coded Visual FractionsEngaging story and colourful illustrations that introduce fractions in a fun and relatable wayFeatures kids characters who share equally, making it easier for children to understand the concept of fractionsClear and colour-coded visual representations of equivalent fractionsLogically ordered, coloured fractions groups for easier learningVisual Comparisons of Colour-coded FractionsClear and easy-to-understand comparisons of fractions and fractions groupsHelps children learn to visually compare and identify different coloured fractionsEquivalent Fractions and Decimal FractionsComprehensive coverage of colour-coded equivalent fractions and decimal fractionsFractions, Equivalent Fractions, Decimal Fractions & PercentagesTeaches children how to compare coloured fractions, equivalent fractions, decimal fractions and percentagesColour-coded Quick QuizzesColour-coded, quick quizzes to check children's understanding of fractionsHelps children retain and apply what they've learnedTarget audience:Ages: 5-11, Kindergarten-5th grades or Year groups 1-6 in primary education (infants, elementary and junior schools).Excellent resource at home or in the classroomA perfect gift for a loved child, visual learner, kids with additional or special educational needs, or someone who find text-based fractions no fun.Purchase:Click the Buy Now button to order a copy.Your purchase is automatically backed up by Amazon's hassle-free money-back guarantee policyBook Details:Engaging activity intended for learners who find text-based fractions no fun90 pagesThe author is an experienced electronics engineer turned a special educational tutor and an author of Visual Maths Fractions to pass his knowledge to other people before he dies and becomes just dust and bones!Also available:Colouring workbook — mybook.to/WB1-Sh-v2Paperback — mybook.to/B-1Colour paperback — mybook.to/B1-CColour ebook —Workbook — mybook.to/WB-1Colour workbook —SERIES1 — UNDERSTANDING FRACTIONS VISUALLY — mybook.to/series12 — ADDING FRACTIONS VISUALLY — mybook.to/series23 — ADDING FRACTIONS STEP-BY-STEP — mybook.to/series34 — UNDERSTAND, ADD & SUBTRACT FRACTIONS VISUALLY — mybook.to/series4PS; Please, don't forget to click the Buy Now button to order your copy with confidence.Thanks for checking. Read more

Prepare to have your mind blown wide open! "Infinity Paradoxes: A Down-to-Earth Guide to Mind-Blowing Math" is the ultimate adventure into the realm of the infinite, where logic bends and reality twists in ways you never imagined possible.Avery Pascal, your witty and brilliant guide, takes you on a thrilling journey through ten mind-bending paradoxes that will forever change how you see the world. From infinite hotels with endless rooms to doubling spheres without breaking the rules, each chapter unravels a new layer of mathematical wonder.Ever wondered if a monkey typing randomly could produce Shakespeare? Or how a vase can be simultaneously full and empty? This book doesn't just pose these questions – it answers them with crystal-clear explanations that will leave you saying, "Aha!" page after page.But don't worry, you won't need a Ph.D. to enjoy this ride. Pascal's down-to-earth approach makes even the most complex concepts accessible and fun. You'll find yourself chuckling at clever anecdotes, nodding along with relatable metaphors, and gasping at the sheer audacity of infinity's tricks."Infinity Paradoxes" isn't just a math book – it's a portal to a new way of thinking. You'll discover how these brain-teasers connect to the real world, from quantum mechanics to economics, reshaping your understanding of the universe and your place in it.Ready to have your mind expanded to infinity and beyond? Dive into "Infinity Paradoxes" today and unlock the secrets of the mathematical universe. Trust us, once you start, you won't be able to stop until you've reached the end – if there is one! Read more

A math prof takes a wild trip to Absolute Infinity...and back. Read more

Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area. Read more

Axiomatic Algebra Without Actual Infinity --- This book broadens applied mathematics from Group Theory to Axiomatic Set Theory by removing actual infinity, because removing actual infinity removes paralyzing holes in logic. Transitioning Axiomatic Set Theory from temporary, experimental pure mathematics into useful applied mathematics completes the formalization of real numbers started by Cantor 150 years ago. -- Modify Cantor’s Continuum Hypothesis by replacing countable infinity with an ever-increasing finite counting natural number and by replacing uncountable infinity with reciprocal of zero, so that positive actual infinity cannot be a quantity of a set. -- Replace “Don’t Divide by Zero” of rational numbers with two axioms that permit 1/0=7+1/0, 1/0=7*1/0, and 2^1/0=3^1/0=1/0 or 0, but not 0/0 because that leads to errors, and have 1/0 the quantity of a set. -- Remove Axiom of Choice so that only bulk operations, like truncation to form an integer, apply to 1/0 quantities. Removing the axiom of choice means there can be no individual operations to a count that is a quantity beyond the largest number yet counted-to. -- Real Numbers have only a finite count of knowable place-value digits both before and after the decimal point. Left of the string of zeros unknowable digits form large-scale imprecision which is akin to infinity (which is not the quantity of set) and can be analyzed using finite numbers. -- Special Relativity. A Lorentz Transformation adds large-scale imprecision to the time-space hyperbolic angle to derive Maxwell’s Equations from the Dirac Equation. Particle properties conform to measured electromagnetic field force and energy. -- That successful application of the axioms to discover a quantum model for 100+ year-old electromagnetism substantiates the new axiomatic algebra is correct and is available for modern in-development theories of physics. ---- Although the math being depicted is quite deep and fundamental, symbols used in the book are nothing beyond what high school students learn in their most advanced math classes. ---- Perhaps what is published in this book should be placed in a technical journal. It isn't in a journal because the author is not familiar with journals. Paul C Daiber is an engineer and is not in academia. As a hobby he has dug into infinity, a feature of math and science that greatly troubled him like it has troubled many of us, and he thinks he has fixed the trouble by restructuring infinity so that it fits into logic. He placed the fix into this book to share it. On Amazon’s free pages please read a summary of what he discovered, and if you want more details there's the rest of the book. \\//, Read more

Are there infinities that are greater than other infinities?One of the first logical reasoning skills that we learn in childhood is to count, so if we get some gift balls to play with, we know how many balls we have, be it one, two, three and so on, because we learn to count units from a young age. and the count increases as we grow.At the end of adolescence we already know how to count numbers as big as we want, since this need to count and quantify is something that is so natural with human beings that we don't even realize the amount of things we are calculating at all times. .Throughout history we find different counting methods associated with different peoples such as the numerical hieroglyphs of the Egyptians, the Babylonian numerical system, Sumerian writing and counting or the Roman numerical system.All these methods were suited to the practical purposes of the time, serving the need to count the days that passed, the cycle of the moon and the tides and the number of animals in a herd but if we asked the citizens of these civilizations what was the number of stars in the sky or grains of sand on a beach there was a conflict of understanding proportions because the concept of infinity was still complex, which continues to this day, even with the concept we have of the universe, galaxies, particles and atoms.In this short but valuable ebook (only 4 pages), you will understand this method called the Hilbert Hotel paradox which is a very interesting mathematical and intuitive thought experiment on infinite sets presented by the German mathematician David Hilbert (1862-1943). Read more

This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions. Read more

Unlock the Secrets of an Ancient Thinker Who Shaped Modern ThoughtAre you ready to challenge your understanding of reality? Zeno of Elea, the brilliant philosopher whose paradoxes have baffled minds for centuries, offers you a journey into the heart of philosophical inquiry. This is not just a book; it’s an intellectual adventure that will change the way you see the world.Dive into the Mind of a Master: Zeno’s paradoxes are more than mere puzzles; they are profound explorations of the concepts of space, time, and infinity. This book breaks down his most famous paradoxes in a way that is accessible to beginners while retaining the depth that scholars crave.Connect Philosophy with Modern Science: Discover how Zeno’s ideas laid the groundwork for modern mathematics and even influenced the development of quantum mechanics. This isn’t just ancient philosophy—it’s the foundation of today’s most cutting-edge scientific thought.Engage with Timeless Ideas: From the first paradox to the latest scientific applications, this book will keep you riveted. Whether you’re a student, a philosopher, or a curious thinker, you’ll find yourself drawn into the intersections of philosophy, mathematics, and science.Join the ranks of those who dare to think differently.Don’t miss out on this opportunity to expand your mind and challenge your perceptions. Zeno of Elea for Beginners is your gateway to understanding the complexities that have intrigued great minds for millennia.Purchase your copy today and embark on a journey that will leave you questioning everything you thought you knew. Read more

In Badiou, Infinity, and Subjectivity: Reading Hegel and Lacan after Badiou, Mohammad Reza Naderi elaborates on the trajectory of Alain Badiou’s philosophy by following a leading thread: the dominance of axiomatic thought and the category of mathematical infinity. According to this primary proposition, axiomatic thought is the only form of thinking adequate to the infinity of being. Using both primary and secondary literature, the author demonstrates two other major propositions: 1) The coherence of Badiou’s intellectual development from the early interventions to the publication of Being and Event, and 2) The formation of a theory Naderi calls “discipline.” By working through three dimensions of disciplinary thinking—interiority, novelty, and beginning—Naderi provides a new framework for understanding the inner structure of what Badiou calls “procedures of truths” and develops a new interpretation that ultimately reveals the inner logic of Badiou’s method. Read more