Re: infinity

Virgil said:
> In article <MPG.1d74edad4517e12698a137@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
> > > In article <MPG.1d6feff9bc68c90398a10f@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >
> > > > Randy Poe said:
> > > > >
> > > > > David Kastrup wrote:
> > > > > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > > > > > > It's the balls inserted AT noon that still remain AT noon.
> > > > > > > That moment is where n becomes infinite.
> > > > > >
> > > > > > There are no balls inserted at noon. Every ball is inserted
> > > > > > before noon.
> > > > >
> > > > > Well, in TO-world, there are balls with infinite-digit natural
> > > > > labels inserted right at noon.
> > > > >
> > > > > But wait... since all balls are inserted at time (1/2)^n before
> > > > > noon, is TO saying that all infinite naturals n have the same
> > > > > value for 2^n?
> > > > Obviously, you mean for 1/2^n, and no, those "zeroes" differ by
> > > > infinitesimal amounts which distinguish them, as points on a line
> > > > may be infinitesimal distances apart.
> > >
> > > Then those balls TO claims are to be inserted infinitesimally
> > > before noon are also to be removed infinitesimally before noon, and
> > > do not remain at noon.
> > >
> > So it may seem from your perspective, and yet, the fact remains that
> > before each removal of a single ball occurs the addition of ten
> > balls, so the number of balls can never decrease to zero under any
> > circumstances given the stated problem.
>
> Then it must either increase to zero or jump to zero, because it
> certainly is zero by noon.

Oh yeah that's it! It increases to zero from a negative amount. So, it is your
idea that there are -9 balls, then you add 10 to get 1, and then remove the 1?
Snazzy!!! How did you get to -9 balls in the vase, and what does that look
like? Does the vase just OWE you nine balls?
>
> > This becomes clear when you
> > remove balls 1, 11, 21, 31, etc, which is precisely the same problem,
> > but with the balls labelled in a way that is actually helpful, rather
> > than confusing to certain sensibilities and therefore clouding the
> > issue.
>
> How is never removing a particular ball, say #2, the same as removing
> it?
Removing a ball is the same as removing a ball. A ball by any other name would
smell as sweet. Shall we fill the vase with roses, so you really get the point?
We'll have Shakespeare arrange the bouquet.
> >
> > This should really be a lesson in one of the major caveats of your
> > approach which seems to be all too often ignored. You can't rely on
> > simple arguments like "every ball corresponding to a natural number
> > is removed before noon".
>
> So that TO refuses to rely on valid statements? What sort of statements
> does he then consider reliable?
There are all sorts of statements that sound valid to the ears that share a
head with the mouth.
>
> > That statement carries with it all sorts of
> > assumptions about infinite sets and numbers which are not necessarily
> > justified to begin with
>
> Then the entire gedankenexperiment does the same, since the statement is
> an immediate and inevitable deduction from the statement of the
> gedankenexperiment itself.
Empty hand waving. Maybe the fruit flies are bugging you, or those little pink
elephants, again?
>
>
>
> > and in this case cause nonsensical results,
> > because they don't even really apply to the problem.
>
> That conclusion is built into the problem itself. Only those who wish to
> violate the very rules of the gedankenexperiment itself instead of
> following them can dispute that the gedankenexperiment REQUIRES that
> "every ball corresponding to a natural number is removed before noon" be
> valid.
Here, try an elephant swatter.

[][][]
88888==========[][][] ~~oP(())\
[][][] iiii
>

--
Smiles,

Tony
.

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