Re: infinity

In article <MPG.1d642dc332cdc21798a045@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> William Hughes said:
> >
> > Tony Orlow (aeo6) wrote:
> > > William Hughes said:
> > > > Tony Orlow (aeo6) wrote:
> > > > > William Hughes said:
> > > > > >
> > > > > > Tony Orlow (aeo6) wrote:
> > > > > > > David Kastrup said:
> > > > > > > > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:
> > > > > > > >
> > > > > > > > > If you want to think of it that way, I suppose you can, even
> > > > > > > > > though
> > > > > > > > > there is no point at which you are taking away more balls
> > > > > > > > > than you
> > > > > > > > > put in. While set theorists claim that order is irrelevant
> > > > > > > > > within a
> > > > > > > > > set,
> > > > > > > >
> > > > > > > > For determining the cardinality of a set the order is
> > > > > > > > irrelevant. It
> > > > > > > > turns out that the cardinality of the set of balls put into the
> > > > > > > > vase
> > > > > > > > and the cardinality of the set of balls taken out again are the
> > > > > > > > same.
> > > > > > > And yet, as Cantorians have admitted in the past, cardinality of
> > > > > > > infinite sets
> > > > > > > is not the same as set size.
> > > > > > >
> > > > > > > > What does this mean? That there is _one_ way of mapping the
> > > > > > > > balls
> > > > > > > > taken in and taken out 1:1. But since this cardinality happens
> > > > > > > > to be
> > > > > > > > infinite, and infinite sets can be mapped to a proper subset of
> > > > > > > > themselves, this does not mean that there might not also be a
> > > > > > > > mapping
> > > > > > > > 1:10. So the question "do balls remain, and how many?" can't
> > > > > > > > be
> > > > > > > > answered by looking just at the set sizes, because the sets are
> > > > > > > > infinite. Instead one has to take a look at every ball
> > > > > > > > individually
> > > > > > > > and has to check whether it will be put in, but not removed.
> > > > > > > > Because
> > > > > > > > we are talking about infinite sets, and the pigeon hole
> > > > > > > > principle is
> > > > > > > > no longer valid.
> > > > > > > So, you look to see if you can ever remove the last ball. When
> > > > > > > you have just
> > > > > > > added 10 balls, removing 1 ball will never result in an empty
> > > > > > > set. Isn't that
> > > > > > > true?
> > > > > >
> > > > > > This is true, but you only add 10 balls at a finite step. No, you
> > > > > > never get the empty set at any finite step. No one disputes this.
> > > > > You never get an empty set at ANY step.
> > > >
> > > > -You never get the empty set at any finite step
> > > > -we only have finite steps
> > > > -you never get an empty set at ANY step
> > > >
> > > > looks like we agree. What I also have is the concept of the
> > > > state after all the finite steps. Call this state, state E
> > > > Which balls are in the vase at state E.
> > > > We do not know, this has to be defined.
> > > >
> > > > Definition 1:
> > > >
> > > > Let I be the union of the sets of balls added to
> > > > the vase at any finite step.
> > > >
> > > > Let O be the union of the sets of balls removed from
> > > > the vase at any finite step.
> > > >
> > > > Then 0 is a subset of I and we define the set of balls
> > > > that is in the vase at state E is the set difference I\O.
> > > >
> > > > How many balls are in the vase at state E?
> > > An infinite number. A larger infinity than the infinite number that have
> > > been
> > > removed.
> >
> > Meaningless words. By definition the number of balls at state E
> > is the number of elements in I\O.
> >
> > My claim is that I\O is empty and contains 0 elements.
> >
> > Which statement do you disagree with?
> >
> > 1. I is a subset of {ball 1, ball 2, ball 3,...}
> agree
> >
> > 2. O is a subset of I
> agree. Insert "proper" before subset.

If O is to be a"proper" subseet of I, there must be some member of I not
in O, but TO is unable to identify any specific such member.
Note that O contains ball 1, and for each nth ball in O, O also
coantains ball n+1, so which ball is missing?
> >
> > 3. I equals the set {ball 1, ball 2, ball 3,...}
> >
> > 4. O equals the set {ball 1, ball 2, ball 3,...}

> these two are not well stated.

Those two are precisely and correctly stated. That TO does not like the
statements is his problem.
> >
> > 5. There is no element in I that is not in O

> disagree

TO is just being disagreeable again.
> >
> > 6. the set difference I\O is empty
> disagree.

TO is just being disagreeable again.
.

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