Re: An uncountable countable set


Tony Orlow wrote:
Virgil wrote:
In article <451b3296@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Randy Poe wrote:
Tony Orlow wrote:
You must have been a strange 10 year old, like that kid
down the block that used to pull the legs off of roaches.

Only those that looked like TO.

So the reason I don't say it's full "an infinitesimal time
before noon" or "some other time before noon" is that
I don't say it's full.
But, you do say it's full or empty, right?

One can easily say that it is empty at any time at which every ball
that was put in has been taken out again.

Does TO suggest that at any time after noon there is any ball that was
put in that was not also taken out?

Yes, at any given time 9/10 of the balls inserted remain.

Which ball does not have a definite time at which it
is removed?

So your conclusion from my statement that I would never
say it's full is that sometimes I would say it's full?
Uh, you would say it contains an infinite number of balls in some
circumstances, as I understand it.

Then you misunderstand it.

No, your labels misconstrue the problem with your silly fixation on
omega. Do I "misunderstand" that if you remove balls 1, then 11, then
21, etc, that the vase will NOT be empty?

We have different variants of the problem setup. Before
discussing too many details, we need to agree on
what EXACTLY are the starting assumptions.

But in general if:
(a) Every ball has a label n which is a finite natural number.
(b) Every ball has a time t_n at which it is removed.
(c) There exists a supremum T of the set {t_n, n in N}
then for any time t >= T, the vase is empty.

If you say it empties, then you would agree that it either fills or it
empties. When does it empty? You say, not before noon. You also say
this does not occur at noon, but after noon there are no balls left. So
when does this occur?

When every ball that was put in has also been taken out again.

At noon or before noon? You're skirting the issue.

In some of our setups, noon is a supremum, and no time
before noon is a supremum. Therefore there is no time
before noon when the vase is empty, and for every
time at noon or after, the vase is empty.

- Randy

.

Relevant Pages

  • Re: An uncountable countable set
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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
    ... Tony Orlow wrote: ... we can say "the last ball was taken out then". ... there are balls in the vase. ... If the vase is empty at noon, but not before, how can that not be the ...
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  • Re: An uncountable countable set
    ... Does Han claim that there is any ball put in that is not taken out? ... the vase empties". ... But in order for the vase to transition from not-empty ... If the vase ever became empty, ...
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  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... we can say "the last ball was taken out then". ... there are balls in the vase. ... If the vase is empty at noon, but not before, how can that not be the moment that it becomes empty? ...
    (sci.math)