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2015-2: Analysis Zero
by Anthony G. O'Farrell. |

Logic does not take direct orders (unless you are ordering in bulk, in which case you should contact us to discuss discounts). The book should be ordered direct from the distributors, Lulu.com. It may also be ordered through any bookseller, including online and bricks-and-mortar retailers (from December 2015). Follow the link below for further details of the book's dimensions and previews of its content.

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Now Professor Emeritus of Maynooth University, he devotes himself to research, writing and pro-bono activities, as well as a modicum of outdoor activity and cultural pursuits. He is married, with three surviving children and seven grandchildren.

This book leads up to the starting-point of a rigorous course in basic real analysis. It is designed to satisfy a student who wants to start 'further back' than the axioms of a complete ordered field. Typically, such a student will be in the second or higher year at University, and will have attained some level of mathematical maturity.

We present a foundation in set theory, and build up through the natural numbers, integers, rational numbers, real and complex numbers, and we establish their properties on the basis of some more basic axioms.

We try to avoid various extremes: The theory is not a 'formal theory', in the strict, logical sense. There are no axioms for the logic used. It is thus a rigorous theory for actual people, not for automata.

It does not try to do the impossible. You have to understand that, because of the work of twentieth-century logicians, we know that we cannot place mathematics on the kind of foundation of which David Hilbert dreamed. That is, it is impossible to give an account of analysis (or of any other sufficiently-rich mathematical theory) which is provably consistent. The only comfort I can offer is that if the theory is inconsistent, then it is already inconsistent by the end of the chapter about the natural numbers,

We do not get involved in the technical discussion of mathematical logic.

We avoid doing 'clever' stuff that violates common-sense notions. For instance, we do not insist that every object under discussion be a set (or even a class).

Some of the ideas and concepts introduced are purely auxiliary, and you can forget about them once you have worked through this book. Indeed, the entire book is designed to be read in a week or two, and then forgotten, unless you are one of the people who want to dig deeper still, and get really serious about logic.

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Updated 11-7-2017

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