Re: infinity

Dave Seaman wrote:

On Tue, 09 Aug 2005 16:55:09 GMT, Kirby Cook wrote:

I spent quite some time explaining to you what an infinite sum actually means.
If you choose not to read what I wrote, then the discussion is over.



If you like. But several times I've had the zero balls position explained to me. 


That's not what this is about.


This is what this is about:

"Is that because you realize that my question is actually relevant to the solution, while yours is nonsense?"

Your question: Can I, or anyone, name the ball or balls in the vase at noon?

The question you call nonsense: Can you or anyone name the last ball removed from the vase?

Your earlier post contained a gross misunderstanding of the meaning of
limit, since you referred to some nonexistent quantity that you called
B_oo(0).  You claimed that this was where the problem was in my argument.

I took the trouble to explain your mathematical error in great detail.
You refused to read it.

For the record, I've read every response you've made to me. When I jumped into this branch of the thread, you were and ever had been responding to another or others.

Instead, you try to pretend that there is such a
thing as a largest natural number, completely oblivious to the fact that
if n is any natural number, then n+1 is a larger one.

I give up.



Not exactly. I believe I'm pointing out that *your* logic implies a last, largest number, since it is *you* who assert that there are zero balls at noon in the same vase in which there were 10 balls added and one ball removed at one minute to noon, while refusing to argue with or even address the salient point that each ball is removed, in its turn, individually.
As I recall, to disprove any assertion, one need only to reduce it to an absurdity, that is, something internally and finally contradictory, such as 1=2. Very well. The balls are removed from the vase one at a time. To get to zero balls by removing one ball, there had to be only one ball left. You claim there cannot be one ball left, but there are, nevertheless, zero balls at noon achieved through the mechanism of removing one ball at a time. That's absurd.

Kirby
.

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. ...
    (sci.math)
  • Re: An uncountable countable set
    ... The mathematics used in the balls and vase problem ... Each ball is put into the vase at a specific ... You think to maniuplate limits in your argumentst. ...
    (sci.math)
  • Re: An uncountable countable set
    ... labelled ball, for example the ball labelled 15, is in the vase at that ... That seems contradictory to me. ... If we had an upper bound on the set of naturals, then if n is a natural ...
    (sci.math)
  • Re: An uncountable countable set
    ... -1/n, where n is a natural number, there are balls in the vase. ... for which we can say "that ball was placed in the vase at time t". ... You cannot proceed to noon without inserting infinite balls, and you cannot empty the vase before noon. ... The only times which may proceed using only finite naturals are those finitely before noon, but at none of those times does the vase empty. ...
    (sci.math)
  • Re: An uncountable countable set
    ... -1/n, where n is a natural number, there are balls in the vase. ... But that *alone* does not even include every time t before noon; ... for which we can say "that ball was placed in the vase at time t". ... though that can be surmised from the insertion and removal ...
    (sci.math)