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 (ε, δ)-definitio ...

, a monad or also a halo is the set of points infinitesimally close to a given point. Given a

hyperreal number In mathematics, hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite if, and only if, , x, for some integer

n

''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 Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object t ...

of ''x''.

References

Nonstandard analysis {{mathanalysis-stub