A new approach in non-standard set theory: The counterfrumentous reals

Lough, Erick T., Mackenzie O’Leary, et. al.
August 4, 2025

Abstract

While the reals have served their purpose for decades—if not millenia—there comes a point in which less-standard approaches must be used to solve those unconventional problems with which modern mathematicians are faced daily. This paper proposes and will attempt to motivate a new alternative: the counterfrumentous reals, a commutative field whose merit across math and physics will be explored in the conclusion of this paper. Evidence suggests a ready understanding of this system has mathematic merit and may have a marked impact on discovery, implementation, and computation times for certain well-suited problems, as well as a not-insignificant impact on broader scopes.