{"product_id":"how-to-measure-the-infinite-mathematics-with-infinite-and-infinitesimal-numbers-hardcover","title":"How to Measure the Infinite: Mathematics with Infinite and Infinitesimal Numbers - Hardcover","description":"\u003cp\u003eby \u003cb\u003eVieri Benci\u003c\/b\u003e (Author), \u003cb\u003eMauro Di Nasso\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.\u003c\/p\u003e\u003cp\u003eThe basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.\u003c\/p\u003e\u003cp\u003eThe book also provides a comprehensive exposition of the \u003cem\u003eTheory of Numerosity\u003c\/em\u003e, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: \"The whole is larger than its parts\". The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.\u003c\/p\u003e\u003ch3\u003eFront Jacket\u003c\/h3\u003e\u003cp\u003eThis book provides a comprehensive exposition of a new way of counting (countable) infinite sets, in particular, numerosities that maintain the ancient Aristotle's principle: \"The whole is larger than its parts.\" It also contains an original introduction to nonstandard analysis. The basic principles are presented in an elementary way by using the ordinary language of mathematics. This is to be contrasted with other introductions, where technical notions from logic are used which are not familiar to most mathematicians. \u003c\/p\u003e\u003cp\u003e This book is the result of a scientific collaboration among different perspectives of mathematics. The first author is a leading figure in variational and topological methods in nonlinear analysis, and has cultivated a broad range of interests in applications of mathematics; while the second author is a specialist in mathematical logic and in the foundations of nonstandard analysis.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 348\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.81 x 9.61 x 6.69 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 27, 2018\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51793367826720,"sku":"9789812836373","price":204.12,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/79f499a449f2680738e8c74bd598bb69.webp?v=1780719649","url":"https:\/\/ebocreations.com\/products\/how-to-measure-the-infinite-mathematics-with-infinite-and-infinitesimal-numbers-hardcover","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}