nonstandard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delt ...

, 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 numbe ...

''x'' in R^∗, the monad of ''x'' is the set :

\text(x)=\.

If ''x'' is finite (limited), the unique real number in the monad of ''x'' is called the

standard part In nonstandard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real. It associates to every su ...

of ''x''.

Notes

References

H. Jerome Keisler: Foundations of Infinitesimal Calculus, available for downloading
Nonstandard analysis {{mathanalysis-stub

See also

Notes

References