In article <email@example.com>, firstname.lastname@example.org wrote:
> On Tuesday, 9 July 2013 01:27:09 UTC+2, fom wrote: > > >> Unless there is some error in that description of the problem, I feel safe > >> in concluding that at noon, no numbers remain in the vase. > > > http://en.wikipedia.org/wiki/Balls_and_vase_problem There are several > > interpretations. > > Why consider such a comparatively involved case (although it is by far more > overwhelming than my case). But my case is so easy to understand that even a > completely perverted matheologian can grasp at least the first dip. > > Insert one by one every natural number into the urn (in always half time like > the room maid of Hilberts hotel cleans all rooms between 11 o'clock and > noon). And take in the same way every natural number out of the urn, but > NEVER take a number out, before the next one has been inserted. Then by > simplest logic you will never have taken out all natural numbers.
That falsely presumes that there must be a last step, either a last insertion or a last removal. But it is also the case that every insertion of a ball is followed by that ball's removal, so that WM is left without being able to identify any ball as having been left in the vase. > > All natural numbers can be taken out. That is > impossible, because even without my ban every natural number taken out has a > larger brother remaining in the urn.
Again WM overlooks that every ball inserted before noon is removed before noon.
The key is to note that such an infinite process cannot be analysed by looking for a last step in the process, but only by looking for an outside step which can only follow after all infinitely many steps within the process are completed. --