Re: Repeating decimals are irrational

wij <wyniijj5@gmail.com> writes:

Snipet from https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber-en.txt/download
>
...
Real Nunmber(ℝ)::= {x| x is represented by n-ary <fixed_point_number>, the
   digits may be infinitely long }
>
   Note: This definition implies that repeating decimals are irrational number.

How does a definition that doesn't mention rational numbers imply
anything about which numbers are rational?

         Let's list a common magic proof in the way as a brief explanation:
           (1) x= 0.999...
           (2) 10x= 9+x  // 10x= 9.999...
           (3) 9x=9    
           (4) x=1
         Ans: There is no axiom or theorem to prove (1) => (2).
>
   Note: If the steps of converting a number x to <fixed_point_number> is not
         finite, x is not a ratio of two integers, because the following
         statement is always true: ∀x,a∈ℚ, x-a∈ℚ
>
---End of quote

Is 1/3 a rational number?

Is 1/3 a real number?

If 1/3 is a real number, what is its representation according to your definition?

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
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