From: wolfgang.mueckenheim@tha.de   
      
   Am 18.12.2025 um 18:53 schrieb Julio Di Egidio:   
   > On 18/12/2025 18:44, wm wrote:   
   >> 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.   
   >   
   > Indeed, Cantor and Hilbert do not prove the existence   
   > of a first and last point of an open real interval,   
      
   But the assumption of actual infinity implies it.   
      
   Regards, WM   
      
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