structure of finite hyperreal numbers

Theorem - Every (or ) hyperreal number x* admits a unique of the form


where a and ϵ is infinitesimalMathworldPlanetmathPlanetmath.

Remark : This theorem just says that every finite hyperreal number has a real partMathworldPlanetmath and an infinitesimal part (just like real and imaginary parts in complex numbersMathworldPlanetmathPlanetmath).

Title structure of finite hyperreal numbers
Canonical name StructureOfFiniteHyperrealNumbers
Date of creation 2013-03-22 17:26:02
Last modified on 2013-03-22 17:26:02
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 4
Author asteroid (17536)
Entry type Theorem
Classification msc 26E35