Re: infinity


Dave Seaman wrote:
> On 8 Aug 2005 13:07:07 -0700, William Hughes wrote:
>
> > Dave Seaman wrote:
> >> On 8 Aug 2005 09:55:44 -0700, William Hughes wrote:
> >>
>
> >> Notice that, unlike the problem posed by Jeremy Boden, we are not told
> >> here that the "oldest" passenger is the one to disembark. Also, the
> >> order has changed: a passenger gets off *first*, unless the subway was
> >> empty when it arrived, and *then* aleph_0 passengers get on.
> >>
>
> > Indeed. In the absence of an ordering rule (e.g. "the oldest passenger
> > must
> > get off") we need some way to force a passenger to get off. Let's use
> > the
> > rule that if there is an immediately preceding step, the first
> > passenger
> > to get on at the immediately preceding step gets off. With this rule
> > the only times the other passengers can be forced to get off is
> > at limit ordinals. Now if there were fewer limit ordinals than
> > passengers the problem would be easy (at least we would know
> > the answer is not 0).
>
> I claim this rule is not needed in order to derive a definite answer.

I agree. My claim is merely that if there are fewer than Aleph_1 limit
ordinals it is easy to get the answer Aleph_1 (for non-limit ordinals
have the first person from the previous step get off. for limit
ordinals
have someone who got on at the first stop get off. This won't work
if there are more than Aleph_0 limit ordinals.) Since there are
Aleph_1 limit ordinals, it is not easy to get the answer Aleph_1
(indeed it is impossible, allthough this has yet to be shown).
Still, the problem would be easy if there were fewer than Aleph_1
limit ordinals.

-William Hughes

P.S. I know the answer

.

Relevant Pages

  • Re: infinity
    ... In the absence of an ordering rule (e.g. "the oldest passenger ... > to get on at the immediately preceding step gets off. ... Now if there were fewer limit ordinals than ... Dave Seaman ...
    (sci.math)
  • Re: infinity
    ... >> Dave Seaman wrote: ... The subway stops at each ... So limit ordinals are the key. ... In the absence of an ordering rule (e.g. "the oldest passenger ...
    (sci.math)
  • Re: infinity
    ... a passenger gets off *first*, unless the subway was ... Now if there were fewer limit ordinals than passengers the problem would be easy. ... I must confess that when I first raised this problem that I was thinking along the lines of labelling the (passenger, station) by a pair of unique numbers. ... this would allow a labelling scheme using positive rational numbers which are of course countable and so the problem remains the same. ...
    (sci.math)