From: wolfgang.mueckenheim@tha.de   
      
   Am 18.12.2025 um 11:20 schrieb Mikko:   
   > 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?   
      
   For every point x < 5 there are points between x and 5. But in actual   
   infinity these points are not created by the attempt to name them. They   
   all are existing with no exception.   
   >   
   > As no defintion of "dark point" is given nothing can be proven about   
   > dark points.   
      
   Dark points are existing but not yet named.   
      
   Regards, WM   
      
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