From: mikko.levanto@iki.fi   
      
   On 18/12/2025 13:57, WM wrote:   
   > 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.   
      
   In the space of the natural numbers there are no points between 4   
   and 5.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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