In nonstandard analysis, a monad or also a 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
monad ( x ) = { y ∈ R ∗ ∣ x − y is infinitesimal } . {\displaystyle {\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.
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