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Titlebook: Real Numbers, Generalizations of the Reals, and Theories of Continua; Philip Ehrlich Book 1994 Springer Science+Business Media Dordrecht 1

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發(fā)表于 2025-3-21 17:24:49 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Real Numbers, Generalizations of the Reals, and Theories of Continua
編輯Philip Ehrlich
視頻videohttp://file.papertrans.cn/823/822182/822182.mp4
叢書名稱Synthese Library
圖書封面Titlebook: Real Numbers, Generalizations of the Reals, and Theories of Continua;  Philip Ehrlich Book 1994 Springer Science+Business Media Dordrecht 1
描述Since their appearance in the late 19th century, theCantor--Dedekind theory of real numbers and philosophy of thecontinuum have emerged as pillars of standard mathematical philosophy.On the other hand, this period also witnessed the emergence of avariety of alternative theories of real numbers and correspondingtheories of continua, as well as non-Archimedean geometry,non-standard analysis, and a number of important generalizations ofthe system of real numbers, some of which have been described asarithmetic continua of one type or another. .With the exception of E.W. Hobson‘s essay, which is concerned with theideas of Cantor and Dedekind and their reception at the turn of thecentury, the papers in the present collection are either concernedwith or are contributions to, the latter groups of studies. All thecontributors are outstanding authorities in their respective fields,and the essays, which are directed to historians and philosophers ofmathematics as well as to mathematicians who are concerned with thefoundations of their subject, are preceded by a lengthy historicalintroduction. .
出版日期Book 1994
關(guān)鍵詞arithmetic; calculus; history of mathematics
版次1
doihttps://doi.org/10.1007/978-94-015-8248-3
isbn_softcover978-90-481-4362-7
isbn_ebook978-94-015-8248-3Series ISSN 0166-6991 Series E-ISSN 2542-8292
issn_series 0166-6991
copyrightSpringer Science+Business Media Dordrecht 1994
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 21:05:12 | 只看該作者
Book 1994standard mathematical philosophy.On the other hand, this period also witnessed the emergence of avariety of alternative theories of real numbers and correspondingtheories of continua, as well as non-Archimedean geometry,non-standard analysis, and a number of important generalizations ofthe system of
板凳
發(fā)表于 2025-3-22 01:09:33 | 只看該作者
A Constructive Look at the Real Number Lineinition of ‘closed subset of ?’ is inappropriate in the constructive setting (6.2); and we devote a considerable amount of space to the property of locatedness, which plays no role whatsoever in traditional analysis (Section 12).
地板
發(fā)表于 2025-3-22 05:37:31 | 只看該作者
On Non-Archimedean Geometrynt and method which are connected to the essence of the principles of pure mathematics and of geometry, upon which it seems to me that geometers have not yet agreed, although these are questions of geometry..
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發(fā)表于 2025-3-22 10:48:57 | 只看該作者
All Numbers Great and Smalls and the ordinals as well as many less familiar numbers including -ω, ω/2, 1/ω, (Math) and ω – πt to name only a few. He further showed that the arithmetic of the reals may be extended to the entire class yielding a ..
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發(fā)表于 2025-3-22 15:51:35 | 只看該作者
On the Infinite and the Infinitesimal in Mathematical Analysishat of delivering an address upon topics chosen by himself to the assembled multitude on Tower Hill. Although my conscience acquits me of having been guilty during my period of office of conduct traitorous to the interests of our Society, I avail myself of the corresponding privilege accorded by our
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發(fā)表于 2025-3-22 19:51:02 | 只看該作者
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發(fā)表于 2025-3-22 22:42:19 | 只看該作者
Veronese’s Non-Archimedean Linear Continuum to Paul du Bois-Reymond and Otto Stolz. (It actually goes back further — consider horn angles in ancient Greece, for example.) The work of du Bois-Reymond was published between 1870 and 1882 (Hahn cites only two articles, 1875 and 1877). That of Stolz appeared from 1879 to 1896 (Hahn cites articles
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發(fā)表于 2025-3-23 05:07:24 | 只看該作者
On Non-Archimedean Geometrytoday since mathematicians such as Poincaré have recognised its importance.. Critics have already recognized its logical validity; therefore, instead of attempting a systematic exposition, as I would have done in Heildelberg, I believe that it is more valuable to focus here on the questions of conte
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發(fā)表于 2025-3-23 09:30:34 | 只看該作者
Calculation, order and Continuityeory, the real algebra of Artin and Schreier (1926). The term ‘real algebra’ refers to an algebraic theory of real numbers; that is to say, an . theory of the conceptual instrument which, from the Greeks to Cantor (and still later), has been used to render the linear . numerical. Real algebra is an
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