Authors: Elemer E Rosinger
Infinitely many {\it ultrapower} field extensions $\mathbb{F}_{\cal U}$ are constructed for the usual field $\mathbb{R}$ of real numbers by using only elementary algebra, thus allowing for the benefit of both infinitely small and infinitely large scalars, and doing so {\it without} the considerable usual technical difficulties involved in setting up the Transfer Principle in Nonstandard Analysis. A natural Integral Calculus - which extends the usual one on the field $\mathbb{R}$ - is set up in these fields $\mathbb{F}_{\cal U}$. A separate paper presents the same for the Differential Calculus.
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[v1] 2014-10-02 04:51:52
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