Re: 3rd Experiment |OR| Infinity

>Suppose you have a giant vase and a bunch of ping pong balls with an integer written on each one, e.g. just like the lottery, so the balls are numbered 1, 2, 3, ... and so on. At one minute to noon you put balls 1 to 10 in the vase and take out number 1. At half a minute to noon you put balls 11 - 20 in the vase and take out number 2. At one quarter minute to noon you put balls 21 - 30 in the vase and take out number 3. Continue in this fashion. Obviously this is physically impossible, but you get the idea. Now the question is this: At noon, how many ping pong balls are in the vase?

At every step you are adding 10 balls and removing 1. This is the same
as saying that you are adding 9 balls at every step. If you repeat this
ad infinitum you end up with an infinite amount of balls in the vase.
Simple as pie.

The corresponding mathematical expression to find the number of balls
after the nth step is

10*n - 1*n

which is obviously the same as 9*n. To find how many balls are there in
the vase at infinity (or as we approach infinity, as you prefer) we
take the following limit:

lim n->oo (10*n-1*n)

Well, if you don't simplify 10*n-1*n, you get with an expression oo-oo
which as we know is *indeterminate*, and which I believe to be the
hidden cause of the debate.

In the other hand, if we simplify the limit to

limit n->oo 9*n

the answer should be obvious.

Oh, and please carry out the experiment with transparent vases. That
should help make evident that we are not getting any closer to
emptiness the more steps we take, and it should help with your friend's
phobia too (full reference:
http://groups.google.com/group/sci.math/browse_frm/thread/2ffb3c24245d7803/a80c935e2d7b1c40#a80c935e2d7b1c40
).

Cheers,
--Tech

.

Relevant Pages

  • Re: An infinite debate
    ... before noon, etc, so that at time noon-1/n the number achieves a value ... saying the same thing I have been saying about it for months. ... The number of balls in the vase is n. ...
    (sci.math)
  • Re: infinity
    ... Physically: Infinity is undefined physically. ... >> to show that each ball is removed from the vase before noon and is not ... >> the vase is empty before noon. ... The operation of adding or removal of balls is undefined at noon. ...
    (sci.math)
  • Re: Questions about the marble problem.
    ... >>>definition of the number of balls in the urn at time s to infinity by ... namely the set of marbles in the vase at that time. ... >> of sets with the property that the cardinality of the set ...
    (sci.math)
  • Re: An uncountable countable set
    ... saying that we should evaluate the limit of Vas t approaches zero ... Do you agree that you are saying that the number of balls in the vase at ... outis the number of balls removed upon completion of iteration n, ...
    (sci.math)
  • Re: Cantor Confusion
    ... Given the information of that Tristram Shandy story, ... vase, even though the vase is more clear about limits. ... intuition, but by logic, that the vase at any time contains more balls ... noon (finished infinity, actualized transfinity) the vase is empty is ...
    (sci.math)