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Re: [Phys-L] irrationals



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