Monad (non-standard analysis)
Encyclopedia
In non-standard analysis
, a monad (also called halo) 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
Non-standard analysis
Non-standard analysis is a branch of mathematics that formulates analysis using a rigorous notion of an infinitesimal number.Non-standard analysis was introduced in the early 1960s by the mathematician Abraham Robinson. He wrote:...
, a monad (also called halo) is the set of points infinitely close to a given point.
Given a hyperreal number
Hyperreal number
The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form1 + 1 + \cdots + 1. \, Such a number is...
x in R*, the monad of x is the set