Editing Superreal number (section)

{{short description|Class of extensions of the real numbers}}
In [[abstract algebra]], the '''superreal numbers''' are a class of extensions of the [[real numbers]], introduced by [[H. Garth Dales]] and [[W. Hugh Woodin]] as a generalization of the [[hyperreal number]]s and primarily of interest in [[non-standard analysis]], [[model theory]], and the study of [[Banach algebra]]s.  The [[Field (mathematics)|field]] of superreals is itself a subfield of the [[surreal number]]s.

Dales and Woodin's superreals are distinct from the [[super-real number (David O. Tall)|super-real number]]s of [[David O. Tall]], which are [[lexicographic order|lexicographically ordered]] fractions of [[formal power series]] over the reals.<ref>{{citation |first=David |last=Tall |title=Looking at graphs through infinitesimal microscopes, windows and telescopes |journal=Mathematical Gazette |volume=64 |issue=427 |pages=22–49 |date=March 1980 |jstor=3615886 |url=http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1980a-microscopes-etc.pdf |doi=10.2307/3615886|citeseerx=10.1.1.377.4224 |s2cid=115821551 }}</ref>