section_path: Extensions of the concept/Nonstandard numbers
section_name: Nonstandard numbers
paragraph_text: Nonstandard numbers
  
  Hyperreal numbers are used in non-standard analysis. The hyperreals, or nonstandard reals (usually denoted as * R), denote an ordered field that is a proper extension of the ordered field of real numbers R and satisfies the transfer principle. This principle allows true first-order statements about R to be reinterpreted as true first-order statements about * R.
  
  Superreal and surreal numbers extend the real numbers by adding infinitesimally small numbers and infinitely large numbers, but still form fields.