hyperreal

Hyperreal refers to extensions or applications of reality that go beyond the ordinary real world in different disciplines. In mathematics, the hyperreal number system, denoted *R, extends the real numbers to include infinitesimal and infinite elements, making it non-Archimedean. It can be constructed as an ultrapower of the real numbers using a non-principal ultrafilter on the natural numbers. The transfer principle ensures that many first-order properties of real numbers hold for hyperreals, providing a rigorous foundation for calculus with infinitesimals and for various models in analysis and probability.

In art, hyperrealism is a style of painting and sculpture that aims to resemble a high-resolution photograph or an exceptionally detailed image. It emerged in the late 20th century and overlaps with photorealism, but often emphasizes heightened realism, technical virtuosity, and sometimes narrative or conceptual content. The term is sometimes used interchangeably with photorealism, though hyperrealism can stress the illusion of reality as something surpassing mere representation.

In philosophy and cultural studies, hyperreality describes a condition in which the distinction between reality and its representations is blurred, with simulations or media constructs becoming more influential than actual events. The concept, associated with theorists such as Jean Baudrillard, is used to analyze advertising, film, virtual environments, and digital media that create compelling yet mediated experiences. The term is widely applied across media studies, sociology, and aesthetics to discuss how simulations shape perception and social life.