Английская Википедия:Beyond Infinity (mathematics book)

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First edition (US)

Beyond Infinity : An Expedition to the Outer Limits of Mathematics is a popular mathematics book by Eugenia Cheng centered on concepts of infinity. It was published by Basic Books and (with a slightly different title) by Profile Books in 2017,Шаблон:R and in a paperback edition in 2018.Шаблон:R It was shortlisted for the 2017 Royal Society Insight Investment Science Book Prize.Шаблон:R

Topics

The book is divided into two parts, with the first exploring notions leading to concepts of actual infinity, concrete but infinite mathematical values. After an exploration of number systems, this part discusses set theory, cardinal numbers, and ordinal numbers, transfinite arithmetic, and the existence of different infinite sizes of sets. Topics used to illustrate these concepts include Hilbert's paradox of the Grand Hotel, Cantor's diagonal argument,Шаблон:R and the unprovability of the continuum hypothesis.Шаблон:R

The second part concerns mathematics related to the idea of potential infinity, the assignment of finite values to the results of infinite processes including growth rates, limits, and infinite series.Шаблон:R This part also discusses Zeno's paradoxes, Dedekind cuts,Шаблон:R the dimensions of spaces, and the possibility of spaces of infinite dimensions, with a mention of higher category theory,Шаблон:R Cheng's research specialty.Шаблон:R

The mathematics is frequently lightened and made accessible with personal experiences and stories,Шаблон:R involving such subjects as the Loch Ness Monster, puff pastry, boating, dance contests, shoes,Шаблон:R "Legos, the iPod Shuffle, snorkeling, Battenberg cakes and Winnie-the-Pooh".Шаблон:R

Audience and reception

The Royal Society judges called Beyond Infinity "a very engaging introduction to a forbidding subject".Шаблон:R Similarly, reviewer Anne Haworth calls it "engaging and readable",Шаблон:R and Wall Street Journal reviewer Sam Kean writes that its "chatty tone keeps things fresh".Шаблон:R It is aimed at a popular audience, not assumed to have a significant background in mathematics, including "the young or those brimming with curiosity"Шаблон:R as well as college or secondary-school students,Шаблон:R although it may be "too elementary for mathematicians or mathematics students".Шаблон:R

As similar reading material, reviewer Andrew James Simoson suggests placing this book alongside The Book of Numbers by John Horton Conway and Richard K. Guy (1996), One Two Three... Infinity by George Gamow (1947), and Really Big Numbers by Richard Schwartz (2014).Шаблон:R

References

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