Exotic \mathbbR refers to a mathematical concept where the standard properties of the real numbers are altered in a specific way. In this context, "exotic" means that the structure of the real numbers is modified to create a new system that still retains some characteristics of the original \mathbbR, but behaves differently under certain operations. One notable example of exotic \mathbbR is the construction of non-standard models of real numbers, which can include infinitesimals and infinite numbers. These models are often studied in the field of mathematical logic and model theory, providing insights into the foundations of mathematics and the nature of number systems.