Re: infinity


Dave Seaman wrote:
> On 7 Aug 2005 19:49:43 -0700, snapdragon31 wrote:
>
> > Dave Seaman wrote:
> >> > There is no such a time that the vase would be empty.
>
> >> Wrong. Noon is such a time. If you disagree, name a ball that is in the
> >> vase at noon.
>
> >> > I hope you can see that the argument "All balls are removed before
> >> > noon." alone is not sufficient to claim that the vase is empty at noon.
>
> >> You keep asserting this, but you have never given any hint as to what it
> >> is that makes you think such a thing. What is the reasoning behind your
> >> outlandish claim?
>
> > It would be easier for you to see if the operation add only 1 ball (not
> > 10) and then take out 1 ball. Assuming that we have 1 ball in the vase
> > initially. You can see that no matter how many times there is always
> > one ball in the vase. The number on the ball in the vase always
> > changes.
>
> No, you have merely shown that there is always a ball in the vase after
> each operation. But since there is no operation taking place at noon,
> your argument is not sufficient to show that there is a ball in the vase
> at noon.
>
> > At 11:59 Ball 1 is in the vase
> > At 11:59:30 Ball 2 is added and ball 1 is removed. Ball 2 remains in
> > the vase.
> > At 11:59:45 Ball 3 is added and ball 2 is removed. Ball 3 leaves in
> > the vase.
>
> > All ball comes into the vase will eventually moved out from the vase
> > but at no time the vase is empty. Therefore, the vase can never be
> > empty. Are you telling me after an infinite steps the vase will become
> > empty? How? My suggestion would be after an infinite number of steps,
> > there would still be 1 ball left in the vase. Can you give me a
> > counter example?
>
> Again, when you say "at no time", you actually mean "at no time before
> noon." In fact, each ball is removed before noon and therefore the vase
> is empty at noon.
>
> Yes, I am telling you that the vase becomes empty at noon, because B(0) =
> sum_{n=1^oo} B_n(0) = 0. Do the math.
>
> >> You also keep ignoring my question. If you think the vase is not empty
> >> at noon, then what is the number of a ball that remains in the vase?
>
> > Not be able to name the number of a ball remains in the vase does not
> > mean that the vase is empty. You can keep all the balls and only take
> > away whatever ball I name at the very last step. It does not prove
> > anything, right? I can prove that the number of balls grow
> > indefinitely, but you cannot prove that the vase is empty.
>
> >> As long as you keep ignoring my question and refuse to provide any
> >> supporting argument of your own, we will never make any progress.
>
> You still have not answered my question, and you still have not provided
> a supporting argument of your own. I rest my case.
>
> --
> Dave Seaman
> Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
> <http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

Hi Dave,

Please don't do the dirty trick again. Your question is to ask for the
number of a ball remaining in the vase. My answer is that I cannot
name the number of that ball. How come you always ignore my answer and
claim that I ignore your question. I gave you the reason why. You say
that I did not provide you a supporting argument. I don't mind if you
don't agree with my point of view. This is the art (or the fun) of
debating. If I can convince you or if you can convince me then this is
not a good paradox. I have no intention to force you to take my point
of view.

>>From my last reply:
"Not be able to name the number of a ball remains in the vase does not
mean that the vase is empty. You can keep all the balls and only take
away whatever ball I name at the very last step. It does not prove
anything, right? I can prove that the number of balls grow
indefinitely, but you cannot prove that the vase is empty."

> Yes, I am telling you that the vase becomes empty at noon, because B(0) =
> sum_{n=1^oo} B_n(0) = 0. Do the math.

Please define what your symbols represent before I can do the math.
My guess would be:
B(0) - Number of balls in the vase at noon.
sum_(n=1^oo) - Your operation A, balls added to the vase before noon
B_n(0) - Your operation B, balls removed from the vase before noon

If my guess is right, should there be a minus sign between the two
operations? That is
B(0) = sum_{n=1^oo} - B_n(0) = 0

I gave a similar answer to someone. The detail is as follow
Let S1 be the set of balls added to the vase
S2 be the set of balls removed from the vase

S1 = {1, 2, 3, ... , OO}
S2 = {1, 2, 3, ... , OO}

Balls remains in the vase would be
S1 - S2 = OO - OO the result is undefined and is not necessary equal to
0.

The result can be anything. If you want the result to be 0 then you
need some kind of proof other than just saying it is.

For example if in each step only 1 ball is added and 10 balls are
removed then the vase will be empty some time before noon provided that
there are not infinite number of ball in the vase initially. It can be
proved mathematically.

If in each step 10 balls are removed first and then 1 ball is added
back then there is no guarantee that the vase is empty at noon because
after each step, exactly 1 ball will stay in the vase.

Please don't take me as your enemy. I am your friend but see things
differently. I am a friend to help you to see more. Similarly, you
are my friend to help me to see more.

.

Relevant Pages

  • 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. ...
    (sci.math)
  • Re: infinity
    ... >> Dave Seaman wrote: ... >> Again this argument alone is not sufficient to claim that the vase is ... >> empty at noon. ... Which ball do you think is in the vase at noon? ...
    (sci.math)
  • 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, ...
    (sci.math)
  • Re: An uncountable countable set
    ... Does Han claim that there is any ball put in that is not taken out? ... the vase empties". ... If the vase ever became empty, ...
    (sci.math)
  • Re: infinity
    ... Number of balls in the vase at noon is f= OO. ... Unfortunately, if infinity gets involved, this statement alone is not sufficient to claim the vase is empty before noon. ... ball) is in the vase. ... You also keep ignoring my question. ...
    (sci.math)