The Logic of Infinity 1st Edition by Barnaby Sheppard (PDF)

Description

Few mathematical results capture the imagination like Georg Cantor’s groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The Logic of Infinity is a fine presentation of some of the concepts and methods “that lie at the logical foundations of mathematics, including the rigorous notions of infinity born in the ground-breaking work of Cantor”, as stated in the introductory pages of the book. This book belongs to that class of publications – increasingly more abundant to the English-speaking audiences- aimed at conveying to audiences not formally trained as a mathematicians but relying on distinct branches of the discipline for their studies, work, or intellectual concerns, some of the immense and rich development of what one may well term modern mathematics. The contemporary fate of continuous specialization within fields and sub-fields of knowledge, is often disadvantageous to fruitful cross-breeding learning from one realm of knowledge to another. The Logic of Infinity is one of those pedagogical works that help to engage a non-mathematician like myself into axiomatic set theory without excessive mathematical language and unprincipled symbol manipulation. It is often said that a book is in essence a vivid conversation with its author (and may I add with several other minds brought into the scene by both author and reader). I am particularly thankful to the author for the “conversations” “we” have so far entertained and to the doors opened to further readings on this and affine topics.

⭐* PhysicalThis book is of a reasonable size of font, printed in B&W and is printed on quality paper, but not the glossy kind.* H.N.D, Undergraduate, Post – Graduate?I would suggest that you would be better to tackle this book and topic area after a year of a mathematical based undergraduate degree.* Descriptions of the bookThis book uses mathematical studies of around 1st – 2nd year degree in a math arena based within functions, sets, logic, limits, simple complex numbers, fundamentals of calculus, and basic number theory to combine and act together as a ladder to build comprehension into the further mathematical explanation topics of infinity. I (i.m.h.o) would encourage you to study and have some of these under your belt already before taking these topics on all at once. It has taken me around a month of almost daily reading to read through this book to get to grips with this area. I still require more studying to grasp some areas, so be aware it’s not a easy read mathematically, even if it is simplifying concepts of infinity. I also suggest you read it start to finish and not jump too much around as its a strong flow of arguments that need consecutive reading and comprehension.I liked the explanations of platonic exploration of can infinity be analyzed within finite, enormous sets (page 154-159). And the items in infinite arithmetic too.* SummaryThe more i read this book, my appreciation of the work involved in writing this book grows. The book is not really necessary for a 1st – Second year math degree study areas as listed before, but it’s good to reflect that applying these previously explained first year / second year entwined mathematical topics in a new way to use this to explore a wide appreciation of the infinity and what it may mean. And improve the understanding of this concepts as a background area to all mathematical areas.

⭐I’m very satisfied.

⭐Le spiegqazioni del libro sono comprensibili solo a chi le cose le sa già. E allora aggiungono poco o niente a ciò che già sapevamo. Troppa carne al fuoco, impedisce all’autore di cucinare qualcosa di commestibile.Absolutely superb as an introduction to the math and philosophical problems of coming to grips with the infinite. Genuinely self-contained, inviting some hard thought on the reader’s part. A book I’d intended to write but he got there first – fair enough! Anyhow, his is probably better!

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