nonstandard analysis

nonstandard analysis (uncountable)

1. (mathematical analysis) Analysis founded upon the hyperreal number system, i.e., which formally defines and uses infinitesimals, especially differentials.
   • 2010 February 25, Joel David Hamkins, “Answer to "How helpful is non-standard analysis?"”, in mathoverflow.net‎, retrieved 2012-11-13:

     To be sure, the epsilon-delta methods arose in part because mathematicians became unsure of the foundational validity of infinitesimals. But since nonstandard analysis exactly provides the missing legitimacy, the original motivation for adopting epsilon-delta arguments appears to fall away.