structure of finite hyperreal numbers

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

$$x=a+ϵ$$

where $a\in ℝ$ and $ϵ$ 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).