Monad (non-standard analysis)

From HandWiki

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

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

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

See also

Notes

  1. ↑ Goldblatt, Robert (1998). Lectures on the Hyperreals. Berlin: Springer. ISBN 0-387-98464-X. 
  2. ↑ NumberPhile, https://www.youtube.com/watch?v=BBp0bEczCNg 

References