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[[File:Standard part function.jpg|thumb|upright=2|right|The standard part function associates to every finite hyperreal, the unique real number infinitely close to it. The bottom line represents the "thin" real continuum. The line at top represents the "thick" hyperreal continuum. The "infinitesimal microscope" is used to view an infinitesimal neighborhood of 0.]]
Nonstandard analysis deals primarily with the [[hyperreal number|hyperreal]] line. The hyperreal line is an extension of the real line, containing infinitesimals, in addition to the reals. In the hyperreal line every real number has a collection of numbers (called a [[monad (
▲Nonstandard analysis deals primarily with the [[hyperreal number|hyperreal]] line. The hyperreal line is an extension of the real line, containing infinitesimals, in addition to the reals. In the hyperreal line every real number has a collection of numbers (called a [[monad (mathematics)|monad]], or '''halo''') of hyperreals infinitely close to it. The standard part function associates to a [[Wikt:finite|finite]] [[hyperreal number|hyperreal]] ''x'', the unique standard real number ''x<sub>0</sub>'' which is infinitely close to it. The relationship is expressed symbolically by writing
:<math>\,\mathrm{st}(x)=x_0.</math>
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*[[H. Jerome Keisler]]: ''[[Elementary Calculus: An Infinitesimal Approach]]''. First edition 1976; 2nd edition 1986. (This book is now out of print. The publisher has reverted the copyright to the author, who has made available the 2nd edition in .pdf format available for downloading at http://www.math.wisc.edu/~keisler/calc.html.)
*[[Robert Goldblatt|Goldblatt, Robert]]: ''Lectures on the [[hyperreal number|hyperreals]]
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