From: wolfgang.mueckenheim@tha.de   
      
   Am 18.12.2025 um 15:59 schrieb Julio Di Egidio:   
   > On 18/12/2025 12:53, WM wrote:   
   >> Am 18.12.2025 um 10:04 schrieb Julio Di Egidio:   
   >>> On 17/12/2025 19:22, wm wrote:   
   >>>   
   >>>> 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.   
   >>>   
   >>> The *existence* is "clearly proven" by the *non-existence* of the first   
   >>> and last point of an open interval... Impeccable logic as usual.   
   >>> [RESTORED]   
   >>   
   >> If all points are existing, then these points are existing too.   
   >   
   > No, only the points that exist do exist, and you still haven't given   
   > a single valid argument for the existence of "extraordinary" points,   
   > not to mention an actually correct proof.   
      
   There is no proof. Actual infinity is an assumption by Cantor and   
   Hilbert: The actual infinity is for instance when we "consider the   
   points of an interval as a totality that is completely existing"   
   [Hilbert, 1925]. Proof is impossible, but the only alternative is   
   potential infinity or even finitism.   
   >   
   >> For every point x < 1 you can find a point between x and 1. These   
   >> points are all existing in actual infinity. They are not generated by   
   >> the attempt to find them.   
   >   
   > Sure *those* point are all existing, what does not exist still is   
   > a first and a last one...   
   >   
   > I won't keep replying if you just come back with more of that,   
   > which even includes some mangling of quotes.   
   >   
   The original quote is this: "die Punkte einer Strecke als eine   
   Gesamtheit von Dingen ansehen, die fertig vorliegt" [Hilbert, 1925].   
      
   Regards, WM   
      
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