Numbers

Name: Numbers
ISBN: 9780387974972

This is a book about numbers - all kinds of numbers, from integers to p-adics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for Â? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th.

Mathematics

Open Library Amazon

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red_trumpetSep 2021
The book Numbers [1] by Ebbinghaus et. al. is a comprehensive treatment, starting from natural numbers up to complex numbers (and quaternions iirc). It also has lots of historic context, how our number systems evolved.
[1] https://www.amazon.com/Numbers-Graduate-Mathematics-Heinz-Di...
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mathgladiatorDec 2010
I recommend the Numbers Book ( http://www.amazon.com/Numbers-Graduate-Texts-Mathematics-Rea... ):
I just did a construction of the integers assuming either sets or arrays. I could equally have used your list definition.
http://pastie.org/1397123 and http://news.ycombinator.com/item?id=2030649
I've very tempted to combine your work with this and then go on to define rationals and then the reals. The reals would be very interesting since it would be a sequence that takes an epsilon and gets a rational number that is close enough. It's kind of crazy to think that all these real numbers are infinite cauchy sequences.
If I define a real as function(eps) { return some_rational; } then I could define it piece_wise and say function mult_real(a,b) { return function(eps) { return a(eps/2) * b(eps/2); } }
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