Monad (nonstandard analysis)


In nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point.[1][2]

Given a hyperreal number x in R, the monad of x is the set

If x is finite (limited), the unique real number in the monad of x is called the standard part of x.[3]

References edit

  1. ^ Goldblatt, Robert (1998). Lectures on the Hyperreals. Berlin: Springer. ISBN 0-387-98464-X.
  2. ^ Wood, Carol (4 Sep 2015). "The Infinitesimal Monad - Numberphile" (video). Numberphile. Retrieved 29 Dec 2022.
  3. ^ Keisler, Howard (19 June 2022). Foundations of Infinitesimal Calculus (PDF). Madison, Wisconsin, USA: University of Wisconsin Press. p. 2. Retrieved 1 March 2024.