Re: infinity

Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> writes:

> I would propose a slightly different problem:
>
> We have two vases, A and B, both initially empty at 1 minute before
> noon. At 1/2 a minute before noon we add 10 balls to vase A, then
> remove a ball from vase A and place it vase B, and repeat this
> process every 1/2^n minutes until noon. In this case, every ball is
> either in vase A or vase B. At noon, how many balls are in vase A
> and how many are in vase B?

Vase A may contain any number of balls (including 0) or it may have
infinitely many balls. Which balls are removed makes all the difference.

Vase B clearly has infinitely many balls.

> How does the labelling affect this scenario?

It gives a convenient means of specifying which balls have been
removed from A.


> If there are zero balls in vase A, are there an infinite number in
> vase B?

There are clearly an infinite number of balls in vase B, regardless of
the number of balls in vase A.

> How can there be more balls in vase B, when vase A always gets a
> larger number of balls at each step?

The cardinalities of the sets in the limit step (noon) is not given as
the limit of the cardinalities.

> Can we have a Cantorian discussion of this scenario? I would like to
> see how this is resolved.

What's a Cantorian discussion?

Anyway, why can't you answer my simple question: In the original
statement of the problem, you claimed there were infinitely many balls
in the vase at noon. Each of these balls has a number written on it.
Surely, you can tell me the number written on one of them, right?

--
"Basically I see myself as a hero in a great drama, and that is part of
how I motivate myself through failures and a lot of negativity, like
from people like you. So the Hammer is part of my own personal story,
my personal myth." -- James S. Harris, a legend in his own mind
.

Relevant Pages

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