Standard part function: Difference between revisions

Revision as of 16:59, 11 October 2010

Revision as of 11:29, 19 October 2010

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The standard part of any [[infinitesimal]] is 0. Thus if N is a [[hypernatural]], then (.1)^N is infinitesimal, and st(.1^N)=0. Similarly, st(0.999...)=1 where there is an infinite hypernatural's worth of 9s.

The existence of the standard part function is a consequence of the [[completeness of the reals]] or the fact that [[finite]] [[closed interval]]s of the reals are [[compact space|compact]].

The standard part function "st" is not an [[internal set|internal object]].