000 02461nam a22003498i 4500
001 CR9781108768863
003 UkCbUP
005 20200127154048.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 190312s2020||||enk o ||1 0|eng|d
020 _a9781108768863 (ebook)
020 _z9781108488068 (hardback)
020 _z9781108738385 (paperback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA241
_b.K6697 2020
082 0 0 _a512.7
_223
100 1 _aKörner, T. W.
_q(Thomas William),
_d1946-
_eauthor.
245 1 0 _aWhere do numbers come from? /
_cT. W. Körner.
264 1 _aCambridge :
_bCambridge University Press,
_c2020.
300 _a1 online resource (xi, 260 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
500 _aTitle from publisher's bibliographic system (viewed on 16 Oct 2019).
505 0 _aIntroduction. The rationals -- The strictly positive rationals -- The rational numbers -- The natural numbers. The golden key -- Modular arithmetic -- Axioms for the natural numbers -- The real numbers (and the complex numbers). What is the problem? -- And what is its solution? -- The complex numbers -- A plethora of polynomials -- Can we go further?
520 _aWhy do we need the real numbers? How should we construct them? These questions arose in the nineteenth century, along with the ideas and techniques needed to address them. Nowadays it is commonplace for apprentice mathematicians to hear 'we shall assume the standard properties of the real numbers' as part of their training. But exactly what are those properties? And why can we assume them? This book is clearly and entertainingly written for those students, with historical asides and exercises to foster understanding. Starting with the natural (counting) numbers and then looking at the rational numbers (fractions) and negative numbers, the author builds to a careful construction of the real numbers followed by the complex numbers, leaving the reader fully equipped with all the number systems required by modern mathematical analysis. Additional chapters on polynomials and quarternions provide further context for any reader wanting to delve deeper.
650 0 _aNumber theory.
650 0 _aMathematics
_xPhilosophy.
776 0 8 _iPrint version:
_z9781108488068
856 4 0 _uhttps://doi.org/10.1017/9781108768863
999 _c525061
_d525059