Am I the only one who thinks this is basically a computational implementation of nonstandard analysis? [edit: There was an excellent reply here which is now de

Am I the only one who thinks this is basically a computational implementation of nonstandard analysis? [edit: There was an excellent reply here which is now deleted, which said essentially that it's not exactly nonstandard analysis. Nonstandard analysis requires you extend R to a field containing infinitesimals. In contrast, all that is necessary here is extending R to an algebra with a nilpotent element (e^2 = 0). http://en.wikipedia.org/wiki/Dual_number http://en.wikipedia.org/wiki/Dual_number ]