Re: An uncountable countable set

Randy Poe wrote:
Tony Orlow wrote:
Randy Poe wrote:
Tony Orlow wrote:
Randy Poe wrote:
Tony Orlow wrote:
Han de Bruijn wrote:
Virgil wrote:

In article <d12a9$451b74ad$82a1e228$6053@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Randy Poe wrote, about the Balls in a Vase problem:

It definitely empties, since every ball you put in is
later taken out.
And _that_ individual calls himself a physicist?
Does Han claim that there is any ball put in that is not taken out?
Nonsense question. Noon doesn't exist in this problem.

Han de Bruijn

That's the question I am trying to pin down. If noon exists, that's when
the vase supposedly empties,
Why does the existence of noon imply there is a time
which is the last time before noon?

It doesn't.

- Randy

I never said it did. When did I say that?
I was responding to Han, who said that "If noon exists, that's when
the vase empties".

Noon exists.

But in order for the vase to transition from not-empty
to empty, there would have to be a last non-empty
moment. That would be the last time before noon.

But there is no "last moment before noon".

So....you're correcting yourself? Okay......


Yes, and at that last moment the last ball would have to be removed,

There is no "last moment" and no "last ball"

There is no spoon, and there is no empty vase, except initially.


and
yet, at the moment before 10 balls would have to have been added. Can
the vase contain -9 balls? :)

There is no "moment before the last moment".

There are successive iteration defined in the problem.


Have you not yet figured out yet that given any two different
times, there are times in between them? That there's no
such thing as the "next moment"?

There are successive iterations. In this gedanken, the next event after 11:59 is 30 seconds later, eh?


I will offer this simple
logical argument. If the vase ever became empty, it would be because one
ball was removed,
Hence my continued statement that the vase does not
"become empty". It is non-empty at certain times and
empty at others.
How do you reconcile....

There is no transitional moment.
...with...

Noon is the first moment at which the vase is empty.
Does the vase not go from non-empty to empty at noon?

No.

So, it stays non-empty?


You're making no
sense. If you can't answer that simple question

I answered it. The answer is "no".

So, it doesn't go from non-empty to empty?


Somebody is asking you to think about infinitely high strips,
and the situation is analogous.

Think about the graph of tan(x), which you may or may not know
grows without bound as x approaches 90 degrees. For values of
x just above 90 degrees, tan(x) is large negative.

Quite. Like 1/x around x=0.


Here's the graph:
http://mathworld.wolfram.com/Tangent.html

If you increase x from 0 to a point just above 90 degrees,
the following things are true:
(a) For every value of x below 90 degrees, y = tan(x) is positive.
(b) For every value of x above 90 degrees, y = tan(x) is negative.
(c) There is no point where y transitioned from positive to
negative.

It did, at 90 degrees, where tan is both positive and negative, given that cos is 0, which is both positive and negative. This is part of the concept with the number circle which makes it intuitively satisfying. It gives continuity to some functions considered discontinuous.


If you plot the number of balls in the vase vs. time, it behaves much
like one of those curves. You have a curve rising asymptotically
toward t = noon, and a flat line at t >= noon. But there is no
"transition" from the rising curve to the flat line, any more than
there is a "transition" from the curve of tan(x), x<90 deg to
tan(x), x>90 deg.

There is no equivalence between oo and 0 (though I have heard people claim otherwise). Between oo and -oo there can sometimes be.


The fact that this bothers you does not constitute my "getting
into trouble".

- Randy


Oh, you're in trouble, Buster.
.

Relevant Pages

  • Re: An uncountable countable set
    ... The only critical time dependency is that each ball to be inserted shall ... the vase is empty at noon of anything of any balls ... An affirmative answer confirms that the vase is empty at noon. ... given the times of insertions and removals. ...
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  • Re: An uncountable countable set
    ... the vase, is consistent with the fact that no balls are removed at noon? ... The only relevant question is "According to the rules set up in the ... is each ball inserted before noon also removed before noon?" ... An affirmative answer confirms that the vase is empty at noon. ...
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  • Re: An uncountable countable set
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  • Re: infinity
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  • Re: An uncountable countable set
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