Monad (non-standard analysis)

In non-standard analysis, a monad (also called halo) 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

• Infinitesimal

References

• H. Jerome Keisler: Foundations of Infinitesimal Calculus, available for downloading