From: mikko.levanto@iki.fi   
      
   On 17/12/2025 20:22, wm wrote:   
   > Am 17.12.2025 um 11:10 schrieb Mikko:   
   >> On 15/12/2025 19:18, wm wrote:   
   >>> The actual infinity is for instance when we "consider the points of   
   >>> an interval as a totality that is completely existing" [Hilbert,   
   >>> 1925]. The points of a line, when completely existing, have a first   
   >>> and a last one because never two or more can exist besides each   
   >>> other. This cannot happen other than by dark points.   
   >> As no definition of "dark point" is given it is possible that no point   
   >> is dark and that every point is dark. The "proof" does not identify   
   >> any feature of a point that would dfferentiate dark from non-dark.   
   >>   
   > Dark points are existing but cannot be identified by their co-ordinates.   
   > The existence of such points is clearly proven by the first and and the   
   > last point of an open interval.   
      
   In the space of hatural numbers there is an interval from the point 4   
   to the point 5. How does the existence of these points prove that   
   there are dark numbers?   
      
   As no defintion of "dark point" is given nothing can be proven about   
   dark points.   
      
   -   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)