The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.

Home Real and Hyperreal Numbers Standard Parts III. Standard Part Principle
 
del.icio.us Reddit Facebook StumbleUpon MySpace Twitter Search the VIAS Library  |  Index

III. Standard Part Principle

Every finite hyperreal number is infinitely close to exactly one real number.

DEFINITION

Let b be a finite hyperreal number. The standard part of b, denoted by st (b), is the real number which is infinitely close to b. Infinite hyperreal numbers do not have standard parts.

Here are some facts that follow at once from the definition. Let b be a finite hyperreal number.

(1)     st(b) is a real number.

(2)      b = st(b) + ε for some infinitesimal ε.

(3)     If b is real, then b = st(b).

Our next aim is to develop some skill in computing standard parts. This will be one of the basic methods throughout the Calculus course. The next theorem is the principal tool.
Home Real and Hyperreal Numbers Standard Parts III. Standard Part Principle

Last Update: 2006-11-05