From: wyniijj5@gmail.com   
      
   On Mon, 2026-01-26 at 01:25 +0100, Janis Papanagnou wrote:   
   > (I probably regret answering to your post.)   
   >    
   > On 2026-01-25 18:20, wij wrote:   
   > >    
   > > You need to prove 4/33 exactly equal to 0.1212..., not approximation.   
   >    
   > Is that all you want proven; a specific example?   
   >    
   > This appears to be as trivial as the more general approach that James   
   > gave and that you (for reasons beyond me) don't accept (or don't see).   
   >    
   > First   
   >      __   
   >    0.12   or   0.1212...   
   >    
   > are just finite representations of real numbers; conventions. And 4/33   
   > is an expression representing an operation, the division. You can just   
   > do that computation (as you've certainly learned at school decades ago)   
   > in individual steps, continuing each step with the remainder   
   >    
   >    4/33 = 0     => 0   
   >    40/33 = 1    => 0.1   
   >    remainder 7   
   >    70/33 = 2    => 0.12   
   >    remainder 4   
   >    40/33 = 1    and at this point you see that the _operations_ *repeat*   
   >    
   > so the calculated decimals (1 and 2) will also repeat. And sensibly we   
   > need a finite representation (see above) to express that.   
   >    
   >    Albert Einstein (for example) said: „Die Definition von Wahnsinn ist,   
   >    immer wieder das Gleiche zu tun und andere Ergebnisse zu erwarten“.   
   >    
   > Are you expecting the sequence of decimals differing at some point?   
   >    
   > If not you see that the number represented by the convention "0.1212..."   
   > equals to the number calculated or expressed by "4/33".   
   >    
   > Janis   
   Not quite sure what you mean.   
      
   https://sourceforge.net/projects/cscall/files/MisFiles/RealNumbe   
   2-en.txt/download   
            3. 1/3 = 0.333... + non-zero-remainder (True identity. How to deny?)   
      
   How would you deny it, and call the cut-off 'equation' identity?   
   You cut off non-zero-remainder to stop repeating, so yes, you see the part you   
   want to see, i.e. the front part without "...", and forgot the definition   
   "infinitely repeat" is invalidated.   
   Let n(i) be the repeating number 0.999... The range [n(i),1] remains 1-1   
   correspondence to [0,1] in each step, nothing changed except scale. Or you   
   suggests every zooming of the small area of Mandelbrot set will be 'empty' or   
   uniform or 'stop' for some mysterious reason.   
      
   I assume you disagee my point in the previous post that every denial must   
   refute Prop 1= Repeating N+N infinitely does not yield natural number.   
          Prop 2= Repeating Q+Q infinitely does not yield rational number.   
                  (precisely, positive rational number)   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)