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