From: david.brown@hesbynett.no   
      
   On 26/01/2026 21:34, wij wrote:   
   > On Mon, 2026-01-26 at 21:07 +0100, David Brown wrote:   
   >> On 26/01/2026 16:51, wij wrote:   
   >>> 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/RealN   
   mber2-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?   
   >>   
   >> Have you ever heard of the concept of "limits" ?  You might want to   
   >> learn something about them before embarrassing yourself.   
   >   
   > What do you know about the concept of "limits"? (You invented? Don't try to   
   be   
   > the next one, again. I remember the other expert in this forum has   
   humiliated himself   
   > once, not sure which one, if I can safely predict. And I ignored the other   
   reply,   
   > because it is too obvious, I leave as record)   
   >   
      
   No, I did not invent the concept of limits.  Newton and Leibnitz were   
   probably the first to use them, then Cauchy formalized them (if I   
   remember my history correctly).  But I /learned/ about them - understood   
   them, understood proofs about them, understood how to use them.   
      
   And more importantly, I learned how mathematics works.  I learned how to   
   read proofs, and how to write proofs.  So I know writing down some   
   statement and claiming "True identity.  How to deny?" does not   
   constitute a proof.   
      
   But I suspect any rational argument will fall on deaf ears here.  You   
   don't understand mathematics, and instead think that you alone have   
   reinvented it and every other mathematician current and historical was   
   wrong.  I would love to be able to help you and cure your delusions, but   
   I have no idea how to do that.  So I will just have to do as others   
   have, and ignore you.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)