"Zeit Geist" <email@example.com> wrote in message news:firstname.lastname@example.org... > On Sunday, July 7, 2013 11:26:34 AM UTC-7, Julio Di Egidio wrote: >> "Zeit Geist" <email@example.com> wrote in message >> news:firstname.lastname@example.org... >> > On Sunday, July 7, 2013 2:59:23 AM UTC-7, muec...@rz.fh-augsburg.de >> > wrote: >> >> >> The old story of the marbles in the urn. In the limit the urn is empty >> >> but the limit of number of marbles is infinite. If limits have to be >> >> calculated by the finite terms, like in mathematics,then this is a >> >> contradiction. >> >> > You mean the Urn where every marble is eventually removed, >> > and at Noon the Urn is empty? >> >> That's indeed a patent logical invalidity, already enough to warrant a >> revision of standard set theory. > > Start with an Empty Urn. > At t = 0, add marbles labeled 1 and 2. > At t = 1/2, remove 1, and add 3 and 4. > At t = 3/4 = 1 - 1/4, remove 2 and add 5 and 6 > > In general; > At t = ( 1 - 1/( 2 ^ n ) )remove marble n, > and add marbles 2n + 1 and 2n + 2. > > You can, easily, use those equations to > find times, t_a and t_r, when any marble is > added and removed.
Indeed, as well as use them to calculate a limit.
> Now, this entire things seems logically invalid, > And IS paradoxical. However, the logic is fine.
You are an idiot: it's the conclusion that I am questioning, not the definitions.
> If you answer "Yes" to those three questions, > then "At t = 1, the Urn is Empty." Is Logically Valid.
Of course I would not answer yes to those questions: the rule is 2 in for each 1 out, so you cannot end up empty by any logic that is a logic.
> If you don't believe that we can Mathematically divide > an interval in half infinitely many time, or have All Natural > Numbers, then you had better re-read all of WM's post; > because everything he says follows from that.
WM does not use logic, but you do not appear very much to the point either.