Re: An uncountable countable set

stephen@xxxxxxxxxx wrote:
Randy Poe <poespam-trap@xxxxxxxxx> wrote:

Tony Orlow wrote:
Mike Kelly wrote:
Tony Orlow wrote:
cbrown@xxxxxxxxxxxxxxxxx wrote:
Tony Orlow wrote:
Virgil wrote:
In article <452d11ca@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

I'm sorry, but I can't separate your statement of the problem from your
conclusions. Please give just the statement.

The sequence of events consists of adding 10 and removing 1, an infinite
number of times. In other words, it's an infinite series of (+10-1).
That deliberately and specifically omits the requirement of identifying
and tracking each ball individually as required in the originally stated
problem, in which each ball is uniquely identified and tracked.
The original statement contrasted two situations which both matched this
scenario. The difference between them was the label on the ball removed
at each iteration, and yet, that's not relevant to how many balls are in
the vase at, or before, noon.
Do you think that the numbering of the balls is not relevant to
determining the answer to the question "Is there a ball labelled 15 in
the vase at 1/20 second before midnight?"

Cheers - Chas

If it's a question specifically about the labels, as that is, then it's
relevant. It's not relevant to the number of balls in the vase at any
time, as long as the sequence of inserting 10 and removing 1 is the same.

Tony
Ah, but noon is not a part of the sequence of iterations. No more than
0 is an element of the sequence 1, 1/2, 1/4, 1/8, ....

The question asks how many balls are in the vase at noon. Not at some
iteration.

Ah, but if noon is not part of the sequence, then nothing from the
sequence has anything whatsoever to do with how many balls are in the
vase at noon.

No, there's one of your leaps again.

That's a particularly weird one.

"If the value at noon doesn't have THIS to do with the
sequence, then it must not have ANYTHING to do with
the sequence".

There's no reason to make such a leap.

- Randy

Actually I think Tony is right on this one. The
sequence Tony is talking about is
1, 9, 18, 27, ...

Uh, starts with 0, but do go on...

This sequence represents the number of balls at times before
noon. The sequence has nothing to do with the number of
balls at noon, as the value for noon does not appear in
the sequence. This is why nobody who argues that the
vase is empty at noon ever mentions such a sequence, and
instead point out the simple fact that each ball added
before noon is removed before noon.

Stephen


So, the infinite sequence of finite iterations where we can actually tell exactly how many balls are in the vase has nothing to do with the vase's state at noon, which is supposed to be the limit of this sequence? Why even mention the gedanken at all then? I suppose every vase is empty at noon, or just whatever you feel like declaring. You're playing silly magic tricks. I'm ashamed for the planet.
.

Relevant Pages

  • Re: infinity
    ... >> Which axioms allow completion of an infinite ... That's what a sequence is, by the way: ... If you do not interrupt the process, the vase never "reaches" noon. ... >> B) Follow the original scenario except that as ball n (which is ...
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  • Re: An uncountable countable set
    ... it's an infinite series of. ... the vase at, or before, noon. ... Do you think that the numbering of the balls is not relevant to ... but noon is not a part of the sequence of iterations. ...
    (sci.math)
  • Re: Cantor Confusion
    ... One that does not ignore the numbering on the balls ... If you want to define the state of the vase after all steps have completed ... "Suppose V = is a sequence of subsets of the natural numbers. ...
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  • Re: An uncountable countable set
    ... it's an infinite series of. ... the vase at, or before, noon. ... Do you think that the numbering of the balls is not relevant to ... as long as the sequence of inserting 10 and removing 1 is the same. ...
    (sci.math)
  • Re: infinity
    ... >>> Which axioms allow completion of an infinite ... That's what a sequence is, by the way: ... > If you do not interrupt the process, the vase never "reaches" noon. ... > where xis the number of balls labeled i. ...
    (sci.math)