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# Surreal Numbers

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Shows how a young couple turned on to pure mathematics and found total happiness. This title is intended for those who might enjoy an engaging dialogue on abstract mathematical ideas, and those who might wish to experience how new mathematics is created.

Paperback, 128 pages

Published
January 1st 1974
by Addison-Wesley Professional

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**Also Sprake JHWH**

All words in a language, all symbols, all operations that can be performed in the language are contained only within the language itself. That is to say, languages are self-defined; their elements are constituted by other elements of the language not by not-words outside the language. Language is therefore a circular affair. Or, more optimistically, language is helical. It refers to itself endlessly and gets more expressive as it does so as it builds upon itself.

Expressive of wha ...more

The characterization is weak, but that hardly matters. It's a nice attempt to both humanize math ...more

The book was about how students should be taught to learn the interesting aspects of the problem rather than to solve it first, how they could train their mind to learn the creative aspects of proofs rather than the proof itself given in textbook.

But after being in a system of 17 year's of examsmanship, I would say I enjoyed his concrete mathematics book better th ...more

actually , I haven't put so much concentration and thought in a book or a novel since Islam between the east and the west which I have not finished so far . but anyway that's not something weird knowing that Donald Knuth of the art of programming is the same gut who wrote it ^_^ it actually adds up :D ...more

The entire book is presented as a dialog between a couple apparently stranded on an island. They find an ancient rock inscribed with:

"In the beginning, everything was void, and J. H. W. H.

Conway began to create numbers. Conway said, "Let

there be two rules which b ...more

It's the idea that counts.

All we have is a bunch of objects ordered neatly in a line,

but we haven't got anything to do with them.

I guess the excitement and the beauty comes

in the discovery, not the hearing.

Rubbish. Wait until you get to infinite sets.

What a miserable night! I kept tossing and turning, and my

mind was racing in circ ...more

Fortunately, that is not at all the point of this novellette, nor does it pretend in any capacity that it is the point. Knuth states, in no uncertain terms, that the book is designed to give the impression of what it is like to do research-level mathematics, where the answers to questions are totally unknown, and there are no resources to research from. Everything must be tried, and sometimes failure is inevitable. It is in thi ...more

I stuck it out.

Knuth - anyone who knows him will attest to this - is good at what he does. Even for someone (me) whose last year of formal math was grade 11, many many years ago, the book was a pleasure. I followed the logic, if not the notation, without too painful an effort (though it was definitely an effort). And the payoff was easil ...more

Surreal numbers (aka hyperreals) are the basis for non-standard analysis, and I get to tell my calculus students about that.

I also love books that combine mathematical work with a story, no matter how simple.

It is playful and invites readers to follow the steps of Alice and Bill and play with mathematical proofs from scratch, creating a whole universe day by day.

A masterly introduction to one of the non standard number systems providing some real insight into what they are and how they work.

Written in the form of a dialogue between two enthusiasts who just happen to be stranded on an island. Full of acerbic comments on the nature of forced education and solid thoughts on how best to learn and do math in general.

Apr 14, 2013
Bowei Zhang
added it

I must admit, I did not finish this book therefore maybe I am not qualified to rate it.

The proofs are elegant and inspiring. But after I read some chapters, I soon realized that Prof. DEK might be not very good at telling stories. The conversations between Alice and Bill were pretty boring and most importantly, lacked habitual humor which could be found in TAOCP or Concrete Mathematics.

The proofs are elegant and inspiring. But after I read some chapters, I soon realized that Prof. DEK might be not very good at telling stories. The conversations between Alice and Bill were pretty boring and most importantly, lacked habitual humor which could be found in TAOCP or Concrete Mathematics.

Other than that, a gentle introduction to surreal numbers

May 14, 2018
John
added it

I had expected the book to at least start explaining why and where such numbers or system is useful, but it goes nowhere near that. Lots of busy-work math proofs isn't quite what I was after.

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## Goodreads is hiring!

Donald Ervin Knuth, born January 10th 1938, is a renowned computer scientist and Professor Emeritus of the Art of Computer Programming at Stanford University.

Author of the seminal multi-volume work The Art of Computer Programming ("TAOCP"), Knuth has been called the "father" of the analysis of algorithms, contributing to the development of, and systematizing formal mathematical techniques for, the ...more

Author of the seminal multi-volume work The Art of Computer Programming ("TAOCP"), Knuth has been called the "father" of the analysis of algorithms, contributing to the development of, and systematizing formal mathematical techniques for, the ...more

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