Construction of the Real Numbers

  • Ethan D. Bloch


Real analysis—which in its most basic form is the rigorous study of the ideas in calculus—takes place in the context of the real numbers, because the real numbers have the properties needed to allow things such as derivatives and integrals to work as we would like them to. A rigorous study of derivatives and integrals requires a rigorous treatment of the fundamental properties of the real numbers, and that is the topic of this chapter and the next.


Real Number Natural Number Rational Number Binary Operation Integral Domain 
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Copyright information

© Springer Science+Businees Media, LLC 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentBard CollegeAnnandale-on-HudsonUSA

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