Re: infinity

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > stephen@xxxxxxxxxx said:
> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >> > stephen@xxxxxxxxxx said:
> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >> >> > stephen@xxxxxxxxxx said:
> >> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >> >> >> > Jesse F. Hughes said:
> >> >> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> >> >> >> >>
> >> >> >> >> >> Why? Was there a last one added? If not, how did the process of
> >> >> >> >> >> adding balls end? The process of taking them out ended the same way:
> >> >> >> >> >> without a final step.
> >> >> >> >> > The process ended at noon. How did the process end?
> >> >> >> >>
> >> >> >> >> The same way the process of putting the balls in ended. Are you
> >> >> >> >> claiming there was a last ball added? If not, why do you ask when the
> >> >> >> >> last ball was removed?
> >> >> >> > because you claim there were balls in the vase, and then it became empty, and
> >> >> >> > you are only removing 1 ball at a time, so there MUST have been a last ball
> >> >> >> > removed.
> >> >> >>
> >> >> >> And you are claiming that the vase started out with a finite number
> >> >> >> of balls, and ended up with an infinite number of balls, and you are
> >> >> >> only adding a net of 9 balls at a time, so there must have been a point
> >> >> >> at which n+9 = oo for some finite n, right?
> >> >> > LOL!!! I suppose if the problem were that we added one ball at a time every 1/2
> >> >> > ^n seconds, that it would never reach infinity either, because of your "no
> >> >> > largest finite number" mantra? Give it up already. That nonsense is not an
> >> >> > excuse or an explanation for any of this absurdity. I can't believe you would
> >> >> > be so short-sighted as to try to raise that tired o;d rotten red herring in
> >> >> > such an obviously irrelevant place.
> >> >>
> >> >> You did not answer the question. For which finite n does n+9 become
> >> >> infinite? You claim that it becomes infinite, and you require
> >> >> that it becomes infinite at some specific step. You cannot
> >> >> demand that we identify the step at which the number of balls
> >> >> becomes zero unless you identify the step at which the
> >> >> number of balls becomes infinite.
> >> > LOL. So, your position is that, if we didn't remove ANY balls at each step, and
> >> > just added 10 each time, that it would STILL not be infinite at noon, because
> >> > we cannot identify the point at which it beomes infinite? Is that your
> >> > position? (Oh, please, say "yes").
> >>
> >> No. Why would you think that?
> >>
> >> If you add 1, or 10 balls, and do not remove any balls, there is no step
> >> in the process that begins with a finite number of balls and ends with
> >> an infinite number of balls. However when noon arrives, there will
> >> be an infinite number of balls in the vase.
> > Look again at what you wrote above. You claim that I claim there is some step
> > where the finite becomes infinite, if I claim the sum is infinite, but you can
> > claim the sum is infinite WITHOUT claiming there exists this finite-infinite
> > step? Something tells me you have two sets of rules, one for you and one for
> > me. What exactly WAS your point, if not that?
>
> My point is that we both agree that despite the fact that
> at no step does the number of balls go from finite to
> infinite that there are an infinite number of balls at noon.
>
> I have only one set of rules. You are the one who picks
> and chooses which rule to apply depending on what answer you
> want. The number of balls at noon is infinite because
> there exists a bijection from the balls to a proper subset of the
> balls. Each ball is labelled with a finite natural number.
> There is no step at which a ball labelled with anything other
> than a finite natural number is added, and there is no step
> at which the number of balls becomes infinite.
>
> >>
> >> Likewise, if we are removing balls, there is no step in the process
> >> that begins with one ball and ends up with zero balls. However
> >> when noon arrives there will be zero balls in the base.
> > There is no step where the vase becomes empty, but the vase becomes empty....
>
> Just as there is no step where the number of balls becomes
> infinite but at the end the number of balls is infinite.
>
> Do you agree with that or not? Is there a step at which
> the number of balls becomes infinite? Is there
> some finite n such that n+9 is infinite? You heartily
> deny this everytime it is brought up, but now you
> are implying that there is some step at which the balls
> become infinite.
The balls, like the natural numbers, become infinite after an infinite number
of steps. All steps before noon are finite, but AT noon, the rate of iteration
becomes infinite, and all infinite steps occur then. An infinite number of
finite steps, or a finite number of infinite steps, is necessary to reach
infinity.
>
> >>
> >> You agree that in the first case there is no step that starts
> >> with a finite number of balls and ends with an infinite number
> >> of balls. Yet you accept that the final result is infinite, despite
> >> the fact that no step actually produces an infinite result.
> > So, what was your question supposed to address? It sounded like a claim that
> > you could never have infinite balls in the vase, because you can never have a
> > finite step bridge the gap between finite and infinite. Now, you claim that the
> > set becomes infinite despite this fact, but I am sure you still cling to the
> > very same non-logic that there can be no infinite naturals because there is no
> > single step that creates an infinite from a finite by finite addition. In the
> > one case, you use logic against me, then dismiss it when directed at you, but
> > then deem it a fine defense when questioned about the finitude of your
> > naturals. Can you please decide one way or the other? Does your largest finite
> > mantra only apply when you feel like it? This inconsistency is ridiculous.
>
> I have said nothing about a largest finite.

It's the same as asking when the finite turns infinite, You certainly did
mention that, and it seemed to be your entire point: another rehashed
ireelevant reference to the zone between finite and infinite. SO what?

> You are again
> confusing the elements of the set with the set itself.
Wrong.
> There is no bridge from finite to infinite. Finite values
> can increase forever and never become infinite. There
> is no finite n such that n+1 is infinite. However
> the set of all finite numbers is infinite. I know you
> do not understand that.
I disagree with your "logic", as it concerns numbers but includes no math.
>
> >> However you reject that the vase could become empty exactly
> >> because there is no step that actually produces a result of zero.
> >> If you were consistent you would also reject that the number
> >> of balls ever becomes infinite, because no step results
> >> in an infinite number of balls. Or you would accept that
> >> the number of balls becomes zero.
> > Um, is it, or is it not possible to get zero by subtracting 1 from 1? Is it
> > possible to empty the vase by removing a ball at a time, and not have a last
> > ball? This is absurdity in perfect form.
>
> Is it possible to get an infinite number of balls by adding
> a finite number of balls to a finite number of balls? At
> every step we start with a finite number of balls, and add
> a finite number of balls.
If you do it an infinite number of times, then you cannot avoid having an
infinite sum.
>
> Why is it necessary that there is a step that results in
> zero balls but it is not necessary that there is a step
> that results in an infinite number of balls?
You are removing the balls one at a time and claiming the vase empties, that's
why.
>
> You also agree that if we start with an infinite number
> of balls and remove them 1 at a time at the specified times
> we end up with zero balls. What is the last ball removed
> in that case?
Depends what the last ball in was. According to the problem schedule, as I've
said, yor infinity would be log2(N), where N is the number of moments ina
minute.
>
> When you use the word 'possible' I wonder if you are
> somehow imagining that this scenario is physically possible.
Don't be stupid.
> It is clearly physically impossible. You cannot move
> balls arbirtarily fast, and there is apparently not enough
> matter in the universe to create an infinite number
> of ping pong balls. So what do you mean by 'possible'?
> The whole situation is physically impossible. Mathematical
> possibility and physical possiblity are not the same thing.
Yeah, so it should seem obvious that I mean mathematically possible, in the
context of the whole of math.
>
> Stephen
>

--
Smiles,

Tony
.

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