|
|
Re: Matheology § 300
Posted:
Jul 7, 2013 4:59 PM
|
|
On Sunday, July 7, 2013 12:57:04 PM UTC-7, Julio Di Egidio wrote:
> "Zeit Geist" <tucsondrew@me.com> wrote in message
>
> news:474a03d7-8d54-4309-92a4-62438801b04b@googlegroups.com...
>
> > On Sunday, July 7, 2013 11:26:34 AM UTC-7, Julio Di Egidio wrote:
>
> >> "Zeit Geist" <tucsondrew@me.com> wrote in message
>
> >> news:28218b93-b279-4a7d-889a-54169b3e928e@googlegroups.com...
>
> >> > 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.
>
Limits are not used here.
I only need for each n, there is a time t_n < 1 such that
marble n I s removed at time t_n; in order to prove
the vase is empty at time t.
>
>
> > 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.
>
I didn't say you were!
Just stating the details here to be clear.
>
> > 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.
>
Look at the questions individually.
Can you do the first one?
Can you do the second?
Answer those without reference to the given Supertask?
Now, answer.
Is the third the case for the given Supertask.
>
> > 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.
>
And you are refusing to accept logical conclusions.
The logic is not broken; it just clashes with you preconceived
intuitions that are founded in the finite.
>
> Julio
ZG
|
|
