{"product_id":"from-counting-to-continuum-what-are-real-numbers-really-paperback-softback-9781009538671","title":"From Counting to Continuum; What Are Real Numbers, Really? (Paperback \/ softback) 9781009538671","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFrom Counting to Continuum\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eWhat Are Real Numbers, Really?\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eWhole numbers, fractions, decimals: we frequently use them, but what are they exactly? Let's explore the core ideas behind them.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eEdward Scheinerman (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009538671, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 12 December 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e232 pages\u003cbr\u003e22.8 x 14.9 x 1.2 cm, 0.34 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'Scheinerman adopts a unique approach to the construction of the numbers from natural to complex by defining and using equivalence relations … Recommended.' J. T. Zerger, Choice\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eUnderstanding the natural numbers, which we use to count things, comes naturally. Meanwhile, the real numbers, which include a wide range of numbers from whole numbers to fractions to exotic ones like π, are, frankly, really difficult to describe rigorously. Instead of waiting to take a theorem-proof graduate course to appreciate the real numbers, readers new to university-level mathematics can explore the core ideas behind the construction of the real numbers in this friendly introduction. Beginning with the intuitive notion of counting, the book progresses step-by-step to the real numbers. Each sort of number is defined in terms of a simpler kind by developing an equivalence relation on a previous idea. We find the finite sets' equivalence classes are the natural numbers. Integers are equivalence classes of pairs of natural numbers. Modular numbers are equivalence classes of integers. And so forth. Exercises and their solutions are included.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 0. Prelude\u003cbr\u003e 1. Fundamentals\u003cbr\u003e 2. N: natural numbers\u003cbr\u003e 3. Z: integers\u003cbr\u003e 4. Zm: modular arithmetic\u003cbr\u003e 5. Q: rational numbers\u003cbr\u003e 6. R: real numbers I, Dedekind cuts\u003cbr\u003e 7. R: real numbers II, Cauchy sequences\u003cbr\u003e 8. R: real numbers III, complete ordered fields\u003cbr\u003e 9. C: complex numbers\u003cbr\u003e 10. Further extensions\u003cbr\u003e Answers to exercises\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52173737165080,"sku":"9781009538671","price":18.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009538671i.jpg?v=1781169271","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/from-counting-to-continuum-what-are-real-numbers-really-paperback-softback-9781009538671","provider":"Freshly Printed Books","version":"1.0","type":"link"}