Re: infinity
- From: "David R Tribble" <david@xxxxxxxxxxx>
- Date: 8 Aug 2005 10:02:19 -0700
Tony Orlow (aeo6) wrote:
> I honestly can't believe that the consensus is that, if you add nine balls an
> infinite number of times, you get zero balls. It's nonsense.
Well, first of all, there is no consensus in this thread; there are
three camps: one camp says that there will be zero balls in the
vase at noon, another camp says that there will be an infinite
number of balls in the vase at noon, and the third camp says the
answer is indeterminate.
Since I belong to the first camp (the "Cantorian" camp, if you will),
I'll point out the very subtle but important point about the problem
that you are missing:
It's not just that we add a net nine balls at each step, it's that
we add some balls and then *remove* a ball. In other words, we're
not adding nine balls to the vase an infinite number of times, but
rather that we're adding an infinite number of balls (ten at each
step) and *removing* an infinite number of balls (one at each step)
as well.
The solution to the problem lies in showing either that some balls
are never removed from the vase (so it contains an infinite number
of them at noon), or that every ball that is added is eventually
removed (so the vase is empty at noon), or that we can't determine
either because the problem is unsolvable.
-drt
.
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