In article <firstname.lastname@example.org>, "LudovicoVan" <email@example.com> wrote:
> "Virgil" <firstname.lastname@example.org> wrote in message > news:email@example.com... > > In article <firstname.lastname@example.org>, > > "LudovicoVan" <email@example.com> wrote: > >> "LudovicoVan" <firstname.lastname@example.org> wrote in message > >> news:email@example.com... > >> > "LudovicoVan" <firstname.lastname@example.org> wrote in message > >> > news:email@example.com... > <snip> > > >> >> Now, again: have you got any set-theoretical statement of the > >> >> Ross-Littlewood problem (for every n, 10 balls get in and 1 gets out) > >> >> from which one can derive (prove) that the set of balls ends up empty > >> >> (i.e. that the cardinality of the limit of this sequence of sets is > >> >> zero)? I won't ask anymore: replies welcome... > >> > > >> > In fact, that is tantamount to saying that the cardinality of the set N > >> > of > >> > natural numbers is zero, as N is (equivalent to) the limit of the > >> > sequence > >> > "for every n, put 2 balls in and take 1 one out" (defined so to satisfy > >> > the paralogism that every ball gets eventually removed, although it is > >> > more commonly the set where "for every n, 1 ball (labeled n) gets in"). > >> > > >> > In short, I still claim, nonsense and surely not a problem with set > >> > theory. > >> > >> BTW, you haven't commented on this one. It seems to me that, if the vase > >> ends up empty in set theory, then set theory is provably inconsistent, > >> not > >> simply unsound. > > > > What is inconsistent about after having removed each item put into the > > vase finding it empty? > > First, that's still a paralogism as far as I can tell. But, if we assume > that it is provable as you say, then on a side you'd have axioms from which > you can derive that a set N of naturals exists and is not empty, so that > card(N)=/=0, while on the other, thanks to the equivalence (bijection) > hinted at above, you can derive card(N)==0. And that is properly an > inconsistency.
You may be able to derive "card(N)==0" using your math, or possibly using WM's WMatheology, but I, using only my own standard math, cannot. --