The Emergence of Number
World Scientific, 1987 - 222 من الصفحات
This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of G del's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
ما يقوله الناس - كتابة مراجعة
لم نعثر على أي مراجعات في الأماكن المعتادة.
Preface to the First Edition
The Totality of Real Numbers
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
addition algebraic appears approximation Arabs arithmetic axiom base Bombelli calculation called Cardano century chapter clear complex numbers concept concerned considered construction continues corresponding counting cube cubic equations decimal Dedekind definition demonstration Diophantos equal equations Euclid example existence expressions fact figure follows Footnote further geometric given gives Greek hand ibid idea incommensurable induction infinite introduced irrational kind known language later least lengths less letters limit magnitudes mathematicians mathematics means measure meno method minus multiplication natural numbers negative objects original particular positive possible present problems produced proof proportion proposition Pythagoras Pythagorean quadratic quantities rational real numbers reference regarded result roots rule seems sequence side similar simply solution solving square theorem things translation treat true unit unknown whole writes