Abstract
In this chapter, our objective will be to extend the field ℝ of real numbers to a field *ℝ in which there are both infinitely small and infinitely large “numbers.” In particular we shall find that it is possible in *ℝ, to define precisely the Leibniz differentials dx, dy and to establish a connection between the differential coefficient dy/dx and the derivative f′(x) of a function y = f(x) at the point x.
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Prestel, A. (1991). Nonstandard Analysis. In: Numbers. Graduate Texts in Mathematics, vol 123. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1005-4_15
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DOI: https://doi.org/10.1007/978-1-4612-1005-4_15
Publisher Name: Springer, New York, NY
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