Re: infinity


Tony Orlow (aeo6) wrote:
> Virgil said:
> > 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 no longer valid.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?
> You tell me what the last one removed is, and I'll tell which remain. Enough of
> that nonsense.
> > > >
> > > > 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.
> Then why did you snip my reasons for them being poorly stated. I guess you
> would like to pretend I had no reason. Par for your course.

Virgil quoted:

these two are not well stated.


What TO orignally wrote was:

these two are not well stated. One could agree,
but it glosses over the details as stated initially.

TO characteriztion of the part Virgil snipped as "my reasons for them
being poorly stated" is silly. TO has yet to give any reasons.

-William Hughes

.

Relevant Pages

  • Re: infinity
    ... >>> Which statement do you disagree with? ... 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 ... Then why did you snip my reasons for them being poorly stated. ...
    (sci.math)
  • Re: infinity
    ... >>Virgil said: ... 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 ... Prev by Date: ...
    (sci.math)
  • Re: infinity
    ... > Virgil said: ... 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 ... >>> disagree ...
    (sci.math)
  • Re: infinity
    ... >Virgil said: ... 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 ... Prev by Date: ...
    (sci.math)
  • Re: infinity
    ... >> Virgil wrote: ... >>> TO must agree that each ball is now inserted before it would have been ... >>> But under this new scheme, the vase is obviously empty at noon. ... > Until you explain what you mean by "10 times infinity", ...
    (sci.math)
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