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Hyperreal numbers are an extension of the Real Numbers to include certain classes of infinite and infinitesimal numbers.
A hyperreal number is said to be finite Iff
for some Integer
.
is said to be infinitesimal
Iff
for all Integers
.
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.