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The Irrationals: A Story of the Numbers You Can't Count on
by
Julian Havil
The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In "The Irrationals," the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have ta
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ebook, 312 pages
Published
July 22nd 2012
by Princeton University Press
(first published June 19th 2012)
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Community Reviews
(showing 1-30)
Do not buy the kindle edition of this book. This a mixed review, where I'm guessing that the paper book would be around a 4-star volume, but the kindle edition would need some generosity to be called a 2. The formatting is really that bad.
The first sign of trouble is when the a book about irrationals could not express the square root of two with switching from the regular font a what looked like a low resolution screen shot about two and a half times the size of the surrounding text. Worse yet, ...more
The first sign of trouble is when the a book about irrationals could not express the square root of two with switching from the regular font a what looked like a low resolution screen shot about two and a half times the size of the surrounding text. Worse yet, ...more
A thorough examination of the history of thought about irrational numbers. Many fascinating and surprising properties of the irrationals are proven; the book also presents some questions about the irrationals that are surprisingly still unanswered. For example, though e and pi were both proven to be transcendental in the 1800s, it is still unknown whether e+pi is irrational, let alone transcendental!
This book seems to be pitched to the layman, but there are equations and detailed proofs on nearl ...more
This book seems to be pitched to the layman, but there are equations and detailed proofs on nearl ...more
This book is more of a reference book than a book to read for pleasure. I skimmed through most of the proofs, but enjoyed much of the discussion. I especially liked the details about the three definitions of real numbers: the set of all infinite decimal expansions, the set of all equivalence classes of Cauchy sequences, and the set of Dedekind cuts.
When ranking the level of difficulty of a mathematical textbook, the phrase “mathematical maturity” is often used. This refers to that general increase in mathematical ability that one expects students to achieve as they study more and more mathematics. The phrase can also be used to describe the mathematical community as a whole as it develops, assimilates and then refines new concepts until they often reach the level of the routine.
One sees this thread throughout mathematics, in this book th ...more
One sees this thread throughout mathematics, in this book th ...more
Aug 27, 2014
Ed Terrell
rated it
really liked it
·
review of another edition
Shelves:
2014,
mathematics
Great book for deep dive into the mathematics and proofs of irrationals. I skipped the proofs and only got half way through the book before calling it quits. You have to have a lot of time on your hands as well as some good background to dig through all of this. On the other hand, I loved his historical treatment of the ideas that form the structure from which calculus could arise.
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Goodreads Feedback: not finishing a book | 6 | 136 | Jul 31, 2013 03:48PM |