In non-standard analysis, a monad (also called halo[1]) is the set of points infinitely 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.