Monad (non-standard analysis)

In non-standard analysis, a monad (also called halo^[1]) is the set of points infinitely close to a given point.

Given a hyperreal number x in R*, the monad of x is the set

$\text{monad}(x)=\{y\in \mathbb{R}^* \mid x-y \text{ is infinitesimal}\}.$

Notes

^ Goldblatt, Robert (1998). Lectures on the Hyperreals. Berlin: Springer. ISBN 038798464X.

References

H. Jerome Keisler: Foundations of Infinitesimal Calculus, available for downloading

Infinitesimals

History	Adequality Infinitesimal calculus Leibniz's notation Integral sign Criticism of non-standard analysis The Analyst The Method of Mechanical Theorems Cavalieri's principle

Related branches of mathematics	Non-standard analysis Non-standard calculus Internal set theory Synthetic differential geometry Constructive non-standard analysis

Formalizations of infinitesimal quantities	Differentials Hyperreal numbers Dual numbers Surreal numbers

Individual concepts	Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field Hyperfinite set Law of Continuity Overspill Microcontinuity

Scientists	Gottfried Leibniz Abraham Robinson Pierre de Fermat Augustin-Louis Cauchy

Infinitesimals in physics and engineering	Infinitesimal strain theory Infinitesimal oscillations of a pendulum

Textbooks	Analyse des Infiniment Petits Elementary Calculus

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Monad (non-standard analysis)

See also

Notes

References