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