# structure of finite hyperreal numbers

Every (or ) hyperreal number $x\in{}^{*}\mathbb{R}$ admits a unique of the form

 $x=a+\epsilon$

where $a\in\mathbb{R}$ and $\epsilon$ is infinitesimal.

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

Title structure of finite hyperreal numbers StructureOfFiniteHyperrealNumbers 2013-03-22 17:26:02 2013-03-22 17:26:02 asteroid (17536) asteroid (17536) 4 asteroid (17536) Theorem msc 26E35