Abstract
Real analysis is founded on the fundamental properties of the real number system. The arithmetic structures one studies in real analysis such as linear spaces and linear algebras are based on the additive structure and multiplicative structure of the reals. On the other hand, the order structure of the reals allows for comparisons of quantities expressed by inequalities. For more complex objects of real analysis such as real functions, positivity of their derivatives and integrals characterize monotonicity, another aspect of order.
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© 1989 Kluwer Academic Publishers
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Luxemburg, W.A.J. (1989). Ordered Algebraic Structures in Analysis. In: Martinez, J. (eds) Ordered Algebraic Structures. Mathematics and Its Applications, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2472-7_11
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DOI: https://doi.org/10.1007/978-94-009-2472-7_11
Publisher Name: Springer, Dordrecht
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