Hyperreal Number

Hyperreal numbers are an extension of the Real Numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number $x$ is said to be finite Iff $\vert x\vert < n$ for some Integer $n$. $x$ is said to be infinitesimal Iff $\vert x\vert < 1/n$ for all Integers $n$.

See also Ax-Kochen Isomorphism Theorem, Nonstandard Analysis

References

Keisler, H. J. ``The Hyperreal Line.'' In Real Numbers, Generalizations of the Reals, and Theories of Continua (Ed. P. Ehrlich). Norwell, MA: Kluwer, 1994.