Hyperinteger

In non-standard analysis, a hyperinteger N is a hyperreal number equal to its own integer part.

Dicussion

The standard integer part function [x] is defined for all real x and equals the greatest integer not exceeding x. By the extension principle of non-standard analysis, there exists a natural extension *[x] defined for all hyperreal x, and we say that x is a hyperinteger if

$x={}^{*}\![x]$.

The set $^{*}\mathbb {N}$ of all hyperintegers is an internal subset of $^{*}\mathbb {R}$. The set of all finite hyperintegers (i.e. $\mathbb {N}$ itself) is not an internal subset.