The Book of Numbers

The Book of Numbers is the title of a book written by John Horton Conway and . It was published in the United States by Copernicus, an imprint of Springer-Verlag New York, Inc. in 1995.Conway and Guy. "The book of numbers". Copernicus. 1995. ISBN 978-0387979939 The book was written "to bring to the inquisitive reader without particular mathematical background an explanation of the multitudinous ways in which the word "number" is used." (p.v in Preface). Varieties of topics related to numbers are shown in the book. It was translated to Japanese as "数の本" in 2012.Conway and Guy, translated by 根上生也. "数の本" 丸善出版 (Maruzen publishing). 2012. ISBN 978-4621062074
In the 1st chapter, "The romance of numbers", names of numbers in English and other languages is discussed. In the section of "Millions, billions, and other zillions" (pp.13-16), -illion numbers are discussed, where they extended the traditional naming system to their original system which can name all the integers.
In the 2nd chapter, "Figures from figures: Doing arithmetic and algebra by geometry", numbers defined with geometry, such as square numbers, triangular numbers, tetrahedral numbers, rhombic dodecahedral numbers, higher dimensional numbers, etc. are introduced. After that, in the section of "Some very large numbers" (pp.59-62), arrow notation (p.60), Ackermann number (p.60), Skewes number (p.61), Graham's number (p.61) are introduced. They define their own chained arrow notation (p.61) and describe that Graham's number is less than 3→3→3→3 (p.62).
In the 10th chapter, "Infinite and infinitesimal numbers", Cantor's ordinal numbers are explained up to the first solution of \(\varepsilon_\alpha = \alpha\), i.e., \(\zeta_0\). After that, cardinal numbers and s are introduced.
== Sources ==
Category:Literature