"LudovicoVan" <email@example.com> wrote in message news:firstname.lastname@example.org... > "LudovicoVan" <email@example.com> wrote in message > news:firstname.lastname@example.org... >> "William Hughes" <email@example.com> wrote in message >> news:firstname.lastname@example.org... >>> On Jul 8, 7:06 pm, "LudovicoVan" <ju...@diegidio.name> wrote: >>>> "William Hughes" <wpihug...@gmail.com> wrote in message >>>> news:email@example.com... >>>> > On Jul 8, 6:44 pm, "LudovicoVan" <ju...@diegidio.name> wrote: >>>> >> "William Hughes" <wpihug...@gmail.com> wrote in message >>>> >>news:firstname.lastname@example.org... >>>> >> <snip> >>>> >>>> >> > There is no step w (nothing happens at time 0). >>>> >>>> >> Not even that the vase is empty? Good grief. >>>> >>>> > Certainly the vase is empty at time 0 and this is the first time >>>> > at which it it empty, however, no balls enter or leave the vase >>>> > at time 0 (it is a consequence of the existence of an ordered >>>> > entity without largest element that you can have a process which >>>> > is completed *by* a certain time, but for which there is no >>>> > time at which a step that completes the process happens). >>>> >>>> It is rather a consequence of your ambiguous language that you are not >>>> even >>>> wrong. Have you got any math to show? >>> >>> Try responding first to >>> >>>> And, incidentally, wouldn't you agree that >>>> |limX|=/=lim|X| is just a wrong conclusion here >>> >>> No, as noted before if we define |A| to be the number >>> of finitely-indexed balls in the set A, the statement is >>> true. >> >> If you define |A| to be the number of finitely-labeled balls in set A, >> then, for coherence to the usual terminology, the set A must be the set >> of finitely-labeled balls. That statement is *at last* false, if not >> utterly nonsensical, should you ever bother to spell it out. >> >> 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.