Re: An uncountable countable set

stephen@xxxxxxxxxx wrote:
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:
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?

Who ever said it was the limit of this sequence?

Why even mention the gedanken at all then?

I am not the one who brought it up. I am not even sure
why people think it has anything to do with set theory.

It doesn't. It's a distinct SEQUENCE of events, not a set without order. Set theory doesn't apply. It's just another example of set theorists trying to claim that everything falls under set theory. This experimant obviously does not. Set theory is incapable of handling the concept of sequence in a well-defined way over such a set.

The whole argument is simply that if -(1/2)^floor(n/10) is
less than zero (the minutes before noon that the ball is added),
then -(1/2)^n is less than zero (the minutes before noon the
ball is removed). This really does not rely on set theory.

No, set theory confuses the issue with its concentration on omega. There is no such distinct size of the finite naturals. The infinite iterations are all compressed to a point in this experiment, and since those operations are a combination of additions and subtractions, set theorists feel entitled to rearrange the events any way that gets them their magical results. It's pitiful.


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.

The only argument I am making is that each ball that is added
before noon is removed before noon.

I don't disagree with that. After the removal of every such ball before noon, nine times as many balls remain as have been removed. That is true for every moment before noon. The conclusion as to what happens AT noon either does, or doesn't, have to do with this fact.

Of course by supposing that
an infinite number of actions can be performed we are playing
silly magic tricks. This is not a physical problem. Insisting
on a physical answer to an unphysical problem is pointless.

Stephen


If we start with a vase full of any number of balls, and remove one ball at each of these -1/2^n times, then it becomes empty at noon, or before if the number of balls is finite. There is no argument about that. However, in this case, no balls is removed without ten more being inserted, so the vase cannot become empty, despite set theoretical shenanigans.
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