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 
.
Hyperreal Number
See also
Ax-Kochen Isomorphism Theorem, Nonstandard AnalysisExplore with Wolfram|Alpha
References
Apps, P. "The Hyperreal Line." http://members.tripod.com/PhilipApps/line.html.Goldblatt, R.; Axler, S.; Gehring, F. W.; and Halmos, P. R. Lectures on the Hyperreals: An Introduction to Nonstandard Analysis. New York: Springer-Verlag.Keisler, H. J. "The Hyperreal Line." In Real Numbers, Generalizations of the Reals, and Theories of Continua (Ed. P. Ehrlich). Norwell, MA: Kluwer, 1994.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1168, 2002.Referenced on Wolfram|Alpha
Hyperreal NumberCite this as:
Weisstein, Eric W. "Hyperreal Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HyperrealNumber.html