Re: An uncountable countable set

In article <453e4a85@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

David Marcus wrote:
Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
Your examples of the circle and rectangle are good. Neither has a
height
outside of its x range. The height of the circle is 0 at x=-1 and x=1,
because the circle actually exists there. To ask about its height at
x=9
is like asking how the air quality was on the 85th floor of the World
Trade Center yesterday. Similarly, it makes little sense to ask what
happens at noon. There is no vase at noon.
Do you really mean to say that there is no vase at noon or do you mean
to say that the vase is not empty at noon?
If noon exists at all, the vase is not empty. All finite naturals will
have been removed, but an infinite number of infinitely-numbered balls
will remain.
"If noon exists at all"? How do we decide?

We decide on the basis of whether 1/n=0. Is that possible for n in N?
Hmmmm......nope.

So, noon doesn't exist. And, there is no vase at noon. I thought you
were saying the vase contains an infinite number of balls at noon.


If the vase exists at noon, then it has an uncountable number of balls
labeled with infinite values. But, no infinite values are allowed i the
experiment, so this cannot happen, and noon is excluded.

So did the North Koreans nuke the vase before noon?

The only relevant issue is whether according to the rules set up in the
problem, is each ball inserted before noon also removed before noon?"

An affirmative confirms that the vase is empty at noon.
A negative directly violates the conditions of the problem.

How does TO answer?
.

Relevant Pages

  • Re: infinity
    ... >> I is the union of a bunch of sets. ... >> Define I_n to be the set of balls added at step n. ... by definition the vase is empty at state E. ... > are an infinite number of sets I_n", ...
    (sci.math)
  • Re: infinity
    ... >> You seem to have pulled the infinite series ... > there are nine more balls in the vase that there were at the end of the ...
    (sci.math)
  • Re: infinity
    ... >>> Which axioms allow completion of an infinite ... That's what a sequence is, by the way: ... > If you do not interrupt the process, the vase never "reaches" noon. ... > where xis the number of balls labeled i. ...
    (sci.math)
  • Re: An uncountable countable set
    ... The number of balls approaches infinity as time ... So, David, you think the fact that balls leave the vase only by being ... from infinite series, ... Very basic logic would hold that, if the vase is not empty at any time t ...
    (sci.math)
  • Re: infinity
    ... the argument that the vase is empty does not rely on any ... >> axioms that complete infinite sequences. ... > adding balls to it. ...
    (sci.math)
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