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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The Hyperreal Lineall draw pictures of the hyperreal line and sketch its construction as an ultrapower of the real line. In the middle part of the article, we shall survey mathematical results about the structure of the hyperreal line. Near the end, we shall discuss philosophical issues concerning the nature and sign

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All Numbers Great and Smallentified each ordinal with the set of all ordinals previously created, so that, 0 = ?, 1 = {0}, … , ω = {0, 1, …}, and so on. More recently, Conway [5, 6] discovered that these two methods can be subsumed under a more general construction which leads to an ordered class of numbers embracing the real

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Rational and Real Ordinal Numbers for the real axis have been constructed by Sikorski [9] and, independently, Klaua [4, 5]. Reference [9] introduced integral and rational ordinal numbers; references [4, 5] introduced integral, rational, and real ordinal numbers. The purpose of these constructions is to extend the real axis into the

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Veronese’s Non-Archimedean Linear Continuums of 1896, 1897 and 1898. Tullio Levi-Civita, as Hahn says, gave an arithmetical representation of Veronese’s continuum in 1892/1893 and 1898 [5, 6]. Finally, Hahn cites Arthur Schoenflies’ article of 1906 [7].

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Calculation, order and Continuityreal algebra achieved a long-standing objective which up until then had been considered as desirable but probably unattainable. I shall then identify the immediate ancestral lines whose convergence gave rise to this new approach to the continuum. Finally, I shall point out that, by providing an alge

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tion, most apparent in the demands for “zero exposure”. One way to open a sustainable and acceptable path between such extreme views is the establishment and application of environmental standards understood as quantitative specifications of target values concerning the environment, referred to as e

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