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 |x|<n for some integer n. x is said to be infinitesimal iff |x|<1/n for all integers n.

See also

Ax-Kochen Isomorphism Theorem, Nonstandard Analysis

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Apps, P. "The Hyperreal Line.", 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 Number

Cite this as:

Weisstein, Eric W. "Hyperreal Number." From MathWorld--A Wolfram Web Resource.

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