Re: infinity

In article <MPG.1d63fa4a86a0d9a198a02c@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Jesse F. Hughes said:
> > "Jesse F. Hughes" <jesse@xxxxxxxxxxxxx> writes:
> >
> > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > >
> > >> Jesse F. Hughes said:
> > >>> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > >>>
> > >>> > Jesse F. Hughes said:
> > >>> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > >>> >>
> > >>> >> > Virgil said:
> > >>> >> >> In article
> > >>> >> >> <MPG.1d618aae41392f57989fe9@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > >>> >> >> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > >>> >> >>
> > >>> >> >> > > Which ball is not covered by that argument?
> > >>> >> >> > N+1 through 10n+9.
> > >>> >> >>
> > >>> >> >> If TO means "n+1 through 10n+9" he is presuming that there is a
> > >>> >> >> last,
> > >>> >> >> nth, step, which is specifically prohibited by the rules.
> > >>> >> >>
> > >>> >> >> And as there is no last step, there is no ball that is not
> > >>> >> >> covered.
> > >>> >> >>
> > >>> >> > Then there is no point at which the last ball is removed. Isn't
> > >>> >> > that
> > >>> >> > correct?
> > >>> >>
> > >>> >> The last ball? What's the number written on that one? When was it
> > >>> >> put in?
> > >>> > "largest finite. largest finite."
> >
> >
> > Let's take a different approach.
> >
> > Let's change the problem slightly. Again, we have an infinite set of
> > ping pong balls, each ball labeled with a natural number. But instead
> > of the old procedure, let's put *all* of the balls into the vase at
> > 11:59 and remove the first one. At 11:59:45, we remove the second,
> > and so on.
> This is the same question Virgil posted a half dozen times in a row.
> >
> > Tony: Is the vase empty or not at noon?
> Yes.
> >
> > If empty, then when was the last ball removed?
> Noon.
> >
> > If not empty, then which balls did we fail to remove?
> None.
> >
> > Can we put infinitely many balls into a vase by doing it one at a time
> > (with increasing speed)? If so, are we able to also empty a vase with
> > infinitely many balls by the same method? (Countably infinite in each
> > case, of course.)
> Yes, but not all countable infinities are the same. This is a basic problem
> with "cardinality".

Does TO claim that there are any two countably infinite sets which are
not bijectable to each other? That is all that cardinality claims about
countably infinite sets, that they are bijectable to each other and to
the set of naturals as the ur-countably infinite set.
.

Relevant Pages

  • Re: An uncountable countable set
    ... Given an infinite set of balls numbered with the infinite set of ... naturals and an "infinitely large" initially empty vase, ... At time t before noon balls 1 through 10 are put into the vase and ... Not a single thought experiment has a "physical analog" as you recall ...
    (sci.math)
  • Re: infinity
    ... >> where n is the number of balls left in the vase. ... It is quite possible for a infinite set to have a proper ... > subset with the same cardnality. ... But even if we devise a complete mapping of N to In and N to Out, ...
    (sci.math)
  • Re: infinity
    ... >>> ping pong balls, each ball labeled with a natural number. ... That is all that cardinality claims about ... > the set of naturals as the ur-countably infinite set. ... bijection is the sole criterion for equality of set sizes. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Given an infinite set of balls numbered with the infinite set of ... naturals and an "infinitely large" initially empty vase, ... At time t before noon balls 1 through 10 are put into the vase and ... nevertheless be attached to a physically meaningful arrangement. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... Given an infinite set of balls numbered with the infinite set of ... naturals and an "infinitely large" initially empty vase, ... At time t before noon balls 1 through 10 are put into the vase and ...
    (sci.math)
Loading