A strict non-standard inequality .999... < 1

Details A strict non-standard inequality .999... < 1 A strict non-standard inequality .999... < 1

2008-11-02

arxiv.org/abs/0811.0164v8

Mathematics

History and Overview

21 pages, 3 figures

Scientific paper

Is .999... equal to 1? Lightstone's decimal expansions yield an infinity of numbers in [0,1] whose expansion starts with an unbounded number of digits "9". We present some non-standard thoughts on the ambiguity of an ellipsis, modeling the cognitive concept of generic limit of B. Cornu and D. Tall. A choice of a non-standard hyperinteger H specifies an H-infinite extended decimal string of 9s, corresponding to an infinitesimally diminished hyperreal value. In our model, the student resistance to the unital evaluation of .999... is directed against an unspoken and unacknowledged application of the standard part function, namely the stripping away of a ghost of an infinitesimal, to echo George Berkeley. So long as the number system has not been specified, the students' hunch that .999... can fall infinitesimally short of 1, can be justified in a mathematically rigorous fashion.

Affiliated with

Also associated with

No associations

Rating

A strict non-standard inequality .999... < 1 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A strict non-standard inequality .999... < 1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A strict non-standard inequality .999... < 1 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-248894