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 numbers and primarily of interest in non-standard analysis, model theory, and the study of Banach algebras.
The field of superreals is itself a subfield of the surreal numbers.
Dales and Woodin's superreals are distinct from the super-real numbers of David O.
Tall, which are lexicographically ordered fractions of formal power series over the reals.
[1] Suppose X is a Tychonoff space and C(X) is the algebra of continuous real-valued functions on X.