Re: An uncountable countable set


"Tony Orlow" <tony@xxxxxxxxxxxxx> wrote in message
news:453e4a3f@xxxxxxxxxxxxxxxxxxxxxx

Yes, David. What else happens in this experiment besides insertions and
removals of naturals at finite times before noon? If the infinite sequence
of events is actually allowed to continue until t=0, then you are talking
about events not indexed with natural numbers, so you're not talking about
the same experiment. If noon is not allowed, and all times in the
experiment are finitely before noon, well, at none of those times does the
vase empty, as we all agree. This is why I am asking when this occurs. It
can't, given the constraints of the problem.

From my reading of this issue the vase is empty at noon, as David Marcus
says. But Tony, I have a question for you. Suppose we put one more ball
into the vase, at any time before noon, and that ball is labeled "oo". At
exactly noon that ball is removed from the vase. At noon is the vase empty
or does it contain the ball labeled "oo"?

-R


.

Relevant Pages

  • Re: An uncountable countable set
    ... removals of naturals at finite times before noon? ... From my reading of this issue the vase is empty at noon, ... into the vase, at any time before noon, and that ball is labeled "oo". ...
    (sci.math)
  • Re: INFINITY Revisited
    ... There is no ball that is added at noon. ... > you said that aleph_0 was the name of infinity for the naturals. ... > decimals each with no last digit printed on them (perhaps this is only ... > with no last digit must be either a repeating rational or an irrational ...
    (sci.math)
  • Re: An infinite debate
    ... Tony Orlow wrote: ... before noon, etc, so that at time noon-1/n the number achieves a value ... of naturals ... There would be a ball for every natural ...
    (sci.math)
  • Re: Cantor Confusion
    ... To say that every ball will be removed, is wrong, because there is ... arbitrarily large naturals. ... interesting in order to find internal contradictions of set theory. ... Please state an internal contradiction of set theory. ...
    (sci.math)
  • Re: Cantor Confusion
    ... To say that every ball will be removed, is wrong, because there is ... arbitrarily large naturals. ... numbers represented by all the bits of the universe. ... There is no largest natural, but certainly the vase problem is trivial, ...
    (sci.math)