- Series: Dover Books on Mathematics
- Paperback: 416 pages
- Publisher: Dover Publications; 1st edition (June 1, 1975)
- Language: English
- ISBN-10: 0486612260
- ISBN-13: 978-0486612263
- Product Dimensions: 5.4 x 1.1 x 8.4 inches
- Shipping Weight: 15.5 ounces (View shipping rates and policies)
- Average Customer Review: 41 customer reviews
- Amazon Best Sellers Rank: #232,730 in Books (See Top 100 in Books)
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Introductory Real Analysis (Dover Books on Mathematics) 1st Edition
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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!
1 star for Kindle
5 for book