Introductory Real Analysis

To give a concrete example: One reviewer has suggested that the theorem "Every infinite set has a countable subset" is proved without stating that the axiom of choice is required. This is certainly a serious lapse of rigour, BUT, in a later page, the author explains the axiom of choice (and several equivalent assertions) and also touches upon the fact that there are some very deep set theoretic questions, not yet fully resolved, concerning this axiom. He goes on to say "The axiom of choice will be assumed in this book. In fact, without it, we will be severely hampered for making various set-theoretic constructions". It is evident that the above theorem is one such construction.

This book emphasizes an intuitive approach to the subject, something which in my opinion is neglected by far too many books. Rigour is necessary but never sufficient to acheive proficiency in math!


An accurate title   November 9, 2000
K. Braithwaite (inkster, MI USA)
4 out of 7 found this review helpful

This is an excellent -- and famous -- introduction to real analysis by one of the century's top mathematicians. This is a teaching book, not a reference. The proofs are mostly given in full, not left as exercises, and the whole thing is very clearly written.

3rd year level; quite suitable for physicists.


Solid Introduction to Analysis   December 26, 2001
C. Metcalf
4 out of 8 found this review helpful

Certainly, this is the classic place to start on Real Analysis. One pro of this book is that the price is quite low. I would say as an introduction this is probably not the optimal book. Yes, I might still reference the book from time to time, but more recent books will almost certainly serve the purpose of an introduction better. A more modern book that is a good substitute is Walter Rudin's Principles of Mathematical Analysis.