Editing Nonstandard analysis (section)

=== Applications to calculus ===
As an application to [[mathematical education]], [[H. Jerome Keisler]] wrote ''[[Elementary Calculus: An Infinitesimal Approach]]''.<ref name="EC" /> Covering [[nonstandard calculus]], it develops differential and integral calculus using the hyperreal numbers, which include infinitesimal elements. These applications of nonstandard analysis depend on the existence of the ''[[standard part function|standard part]]'' of a finite hyperreal {{mvar|r}}. The standard part of {{mvar|r}}, denoted {{math|st(''r'')}}, is a standard real number infinitely close to {{mvar|r}}. One of the visualization devices Keisler uses is that of an imaginary infinite-magnification microscope to distinguish points infinitely close together.