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Named set of points in nonstandard analysis
In
nonstandard analysis, a monad or also a halo is the set of points infinitesimally close to a given point.
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Given a
hyperreal number x in R∗, the monad of x is the set
![{\displaystyle {\text{monad}}(x)=\{y\in \mathbb {R} ^{*}\mid x-y{\text{ is infinitesimal}}\}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61d389546d7ae2acf2ce40acac3bbc6c83ca886e)
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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