In article <email@example.com>, firstname.lastname@example.org wrote:
> On Monday, 8 July 2013 22:20:31 UTC+2, Virgil wrote: > > > > Look at this simple piece of logic: If I remove a number ONLY after > > > another one has been inserted, then even infinitely many transactions > > > will NEVER show an empty set. > > > WM's excessively finitist WMytheology is far too restrictive and > > self-contradictory to allow for a proper analysis of this problem. Let WM > > answer this: If every insertion of a natural number into an initially empty > > vase before noon is followed by its removal, also before noon, as is the > > case here, which natural numbers does WM claim will remain unremoved at > > noon? > > I do not order what will have to remain. I order that at least one natural > will remain.
In order for a natural to remain, it must be a natural with no successor, since for every natural WITH a successor, its removal satisfies all of WM's requirements, and thus must occur.
Play the game as long as it is possible without removing all > naturals from the urn. It will possible for the first 10^100^1000^1000000000 > steps. I cannot see that there is a limit. But if you believe that at noon > all naturals will have left the urn, then there must be a limit.
WM is thus claimg the existence of a last natural, one with no successor natural. > > Find it! Tell it!
WM is the only one who claims existence of a natural with no successor, so he is the only one obligated to prove its existence.
Those of us who claim the sequence has no last member have nothing to prove, since every natural EXCEPT FOR a last one is correctly removed from the vase.. --