Re: infinity

In article <MPG.1db86ea17133e01498a48e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Randy Poe said:

> > The situation is not physically realizable. It's about the cardinality
> > of two sets. And what we are saying is that they have the same
> > cardinality. In terms of balls, that means that for every ball
> > put in, we can identify a specific time at which it is removed
> > before noon.

> When you say the cardinality is the same, does that directly translate to the
> same number of balls?

Insofar as "number" can be applied to Dedekind infinite sets, it does.

> I am told that aleph_0 is an equivalence class, rather
> than an infinite number.

There is no reason it cannot be both, if ones definition of "number" is
wide enough.

> Can't the two sets of balls, those put in and those
> taken out, have the same equivalence class, and not the exact same number of
> balls.


NO!

> There seems to be considerable unnecessary conflation here.

Only in TO's mind. Not elsewhere.
> >
> > > I'm having difficulty at saying what the cardinality of the set A of the
> > > balls in the vase at noon is because I can't clearly see what this set
> > > is.
> >
> > Let T(n) = time at which ball n is put in the vase.
> > Let R(n) = time at which ball n is removed from the vase.
> >
> > The set A is the set {n in N: Y(n) < noon and N(n) > noon}
> >
> > > Does it even exist? I think so. But how is it defined?
> >
> > See above.
> >
> > > There's a
> > > big leap from the statement of the problem to the claim A=N-N.
> >
> > It isn't defined as "N-N". Like any set, it is defined by its
> > membership rule. And that is very simple. If a ball is in the
> > vase at noon, then it was put in by noon and not taken out by
> > noon. I can't really see another or simpler test for membership
> > in the set. Do you really think it's a leap to say that a ball
> > is in a vase if and only if it was put in but not taken out?
> >
> > Once you accept that definition, it follows immediately that
> > A is empty.
> >
> > - Randy
> >
> >
.

Relevant Pages

  • Re: An infinite debate
    ... before noon, etc, so that at time noon-1/n the number achieves a value ... saying the same thing I have been saying about it for months. ... The number of balls in the vase is n. ...
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  • Re: An uncountable countable set
    ... saying that we should evaluate the limit of Vas t approaches zero ... Do you agree that you are saying that the number of balls in the vase at ... outis the number of balls removed upon completion of iteration n, ...
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  • Re: An uncountable countable set
    ... I would interpret this as saying that we should evaluate the limit of Vas t approaches zero from the left, i.e., ... Do you agree that you are saying that the number of balls in the vase at ... inis the number of balls inserted upon completion of iteration n, ...
    (sci.math)
  • Re: infinity
    ... >> integer written on each one, e.g. just like the lottery, so the balls ... >> how many ping pong balls are in the vase? ... >number of balls in the vase keep growing to infinity as you approach noon. ... in the sense that the cardinality of the limit of a sequence of sets ...
    (sci.math)
  • Re: infinity
    ... > infinity balls in his vase. ... has probability zero but is possible. ... where every possibility for the cardinality at noon has nonzero ... > where n is the number of balls left in the vase. ...
    (sci.math)
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