example of infinite hyperreal number

The hyperreal number {n}n* is (or ).

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

Given any positive a we have that {n:na} is finite, so {n:a<n} and therefore {a}n<{n}n.

Thus {n}n is infiniteMathworldPlanetmath.

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