Re: infinity

"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.

Tony: Is the vase empty or not at noon?

If empty, then when was the last ball removed?

If not empty, then which balls did we fail to remove?

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.)

--
"[Criticizing JSH's mathematics will result in] one of the worst debacles in
the history of the world. It is foretold in most mythologies and religions.
And yes, you are the ones, the cursed ones, who destroy the world."
--James S. Harris reads from the Aztec Book of the Damned Mathematicians
.

Relevant Pages

  • Re: infinity
    ... >> I is the union of a bunch of sets. ... >> Define I_n to be the set of balls added at step n. ... by definition the vase is empty at state E. ... > are an infinite number of sets I_n", ...
    (sci.math)
  • Re: infinity
    ... >>> Which axioms allow completion of an infinite ... That's what a sequence is, by the way: ... > If you do not interrupt the process, the vase never "reaches" noon. ... > where xis the number of balls labeled i. ...
    (sci.math)
  • Re: An uncountable countable set
    ... The number of balls approaches infinity as time ... So, David, you think the fact that balls leave the vase only by being ... from infinite series, ... Very basic logic would hold that, if the vase is not empty at any time t ...
    (sci.math)
  • Re: infinity
    ... the argument that the vase is empty does not rely on any ... >> axioms that complete infinite sequences. ... > adding balls to it. ...
    (sci.math)
  • Re: Logarithm of transfinite numbers
    ... infinite number of finite numbers. ... balls in the vase, whether n is finite or infinite. ... Yes, and at any given finite n, you have 9n balls in your vase. ... At the end of time T, Tony, is the bin empty ...
    (sci.math)