Editing Nonstandard analysis (section)

=== Pedagogical ===
[[H. Jerome Keisler]], [[David Tall]], and other educators maintain that the use of infinitesimals is more intuitive and more easily grasped by students than the [[Limit of a function#(ε, δ)-definition of limit|"epsilon–delta" approach]] to analytic concepts.<ref name="EC">H. Jerome Keisler, ''[[Elementary Calculus: An Infinitesimal Approach]]''. First edition 1976; 2nd edition 1986: [http://www.math.wisc.edu/~keisler/calc.html full text of 2nd edition]</ref> This approach can sometimes provide easier proofs of results than the corresponding epsilon–delta formulation of the proof. Much of the simplification comes from applying very easy rules of nonstandard arithmetic, as follows:

::infinitesimal × finite = infinitesimal

::infinitesimal + infinitesimal = infinitesimal

together with the [[transfer principle]] (discussed further below).

Another pedagogical application of nonstandard analysis is [[Edward Nelson]]'s treatment of the theory of [[stochastic processes]].<ref name="Ele">Edward Nelson: ''Radically Elementary Probability Theory'', Princeton University Press, 1987, [http://www.math.princeton.edu/~nelson/books/rept.pdf full text]</ref>