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Re: [Phys-L] irrationals



Is there a math-l ?

On Tue, Sep 12, 2017 at 1:02 PM, brian whatcott <betwys1@sbcglobal.net>
wrote:

To quote Catz & Catz cited earlier:

"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. "


:-)
Brian W


On 9/12/2017 10:00 AM, Chuck Britton wrote:

If you think that 1.9999... is NOT identical to 2 then it behooves you
to present a number that falls between these other two numbers.

If you think that infinite expansions should not be a part of the
particular mathematical system that you are currently using, then that is
fine. The you are not allowed to use the form of infinite expansions.




On Sep 11, 2017, at 7:46 PM, brian whatcott <betwys1@sbcglobal.net>
wrote:

Perhaps it would be helpful to creep up on a structure of irrational
lengths - say a square of area 2. It is easy to specify rectangles of
rational length that enclose slightly different areas: 7/5 and 10/7;
141/100 and 200/141; 1414 /1000 and 2000/1414 ; 14142136 /10000000 and
2000000/14142136 and so on.
Which reminds me that mathematicians may insist that a recurring
fraction of this form: 1.9999... is identical to 2 see
https://arxiv.org/abs/0811.0164

Brian W

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_______________________________________________
Forum for Physics Educators
Phys-l@mail.phys-l.org
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