In
nonstandard analysis, a monad (also called halo)
is the set of points infinitesimally close to a given point.
Given a
hyperreal number
In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains number ...
''x'' in R
∗, the monad of ''x'' is the set
:
If ''x'' is finite (limited), the unique real number in the monad of ''x'' is called the
standard part of ''x''.
See also
*
Infinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally ref ...
Notes
References
H. Jerome Keisler: Foundations of Infinitesimal Calculus, available for downloading
Nonstandard analysis
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