Another look at the hyperreal numbers and their applications
When Sir Isaac Newton & Wilhelm Gottfried Leibniz were working on Calculus, they introduced the idea of infinitesimals, (which was later expanded to hyperreal numbers), which was later adapted by Dr. Abraham Robinson in 1960 for use in nonstandard analysis. The use of infinitesimals in Calculus was later replaced with a limit definition because of its lack of a logical foundation. Its resurgence back into valid mathematics can be attributed to Dr. Robinson. We will examine the hyperreal numbers not only to confirm this validity, but also to look for the non-mathematical benefits of this extension of the real numbers.
Arthur Ray Schultz,
"Another look at the hyperreal numbers and their applications"
ETD Collection for Tennessee State University.