Monad (non-standard analysis)

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In non-standard analysis, a monad (also called halo[1]) [2] is the set of points infinitesimally close to a given point.

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

\text{monad}(x)=\{y\in \mathbb{R}^* \mid x-y \text{ is infinitesimal}\}.

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

See also[edit]


  1. ^ Goldblatt, Robert (1998). Lectures on the Hyperreals. Berlin: Springer. ISBN 0-387-98464-X. 
  2. ^ NumberPhile