From: david.brown@hesbynett.no   
      
   On 27/01/2026 23:52, Lawrence D’Oliveiro wrote:   
   > On Tue, 27 Jan 2026 16:31:47 -0000 (UTC), Waldek Hebisch wrote:   
   >   
   >> Actually, part that is needed here is ancient, due to Eudoksos.   
   >> Namely, real numebers a and b are equal if and only if comparing   
   >> them with rational numbers gives the same result.   
   >   
   > They didn’t know about “real” numbers back then. He was talking about   
   > “irrational” numbers.   
      
   Indeed.  They certainly knew about irrational numbers - according to   
   legend, the first Greek to prove that the square root of 2 is not   
   rational was killed for the heresy!  But knowing that there are numbers   
   that are not rational is not enough to complete the reals.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)