example of infinite hyperreal number

The hyperreal number ${\{n\}}_{n\in \mathbb{N}}\in {}^{*}ℝ$ is (or ).

Proof : Let $ℱ$ be the nonprincipal ultrafilter in the entry (http://planetmath.org/Hyperreal).

Given any positive $a\in ℝ$ we have that $\{n\in \mathbb{N}:n\le a\}$ is finite, so and therefore .

Thus ${\{n\}}_{n\in \mathbb{N}}$ is infinite.$\mathrm{\square }$

Title	example of infinite hyperreal number
Canonical name	ExampleOfInfiniteHyperrealNumber
Date of creation	2013-03-22 17:25:59
Last modified on	2013-03-22 17:25:59
Owner	asteroid (17536)
Last modified by	asteroid (17536)
Numerical id	5
Author	asteroid (17536)
Entry type	Example
Classification	msc 26E35