Definition
Nonstandard analysis deals primarily with the hyperreal line. The hyperreal line is an extension of the real line, containing infinitesimals, in addition to the reals. In the hyperreal line every real number has a collection of numbers (called a monad, or halo) of hyperreals infinitely close to it. The standard part function associates to a finite hyperreal x, the unique standard real number x0 which is infinitely close to it. The relationship is expressed symbolically by writing
The standard part of any infinitesimal is 0. Thus if N is an infinite hypernatural, then 1/N is infinitesimal, and st(1/N) = 0.
If a hyperreal is represented by a Cauchy sequence in the ultrapower construction, then
Read more about this topic: Standard Part Function
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