Re: infinity

Hi David. It is correct to say that the number of balls tends to
infinity as we approach noon does not imply that the vase is not empty
at noon. That is why I say 'from a physical point of view' (or in
reality). If we have balls in the vase before noon and there are more
balls going in than coming out. In reality, at noon time the vase
would not be empty.

According to this problem, noon is not reachable. The operation is
undefined exactly at noon. Therefore, even no ball is being taken out
from the vase, you still can claim that there are no ball in the vase
at noon.

Take a look at function Y = (X^2 - 4)/(X - 2)
We know that Y = X + 2 when X not = 2 and Y is undefined at X = 2.
You can put whatever value to Y at X = 2 as you wish. It is perfectly
okay say Y = 0 at X = 2.

If Y = (X^2 - 4)/(X - 2) is an equation to represent a real event then
we would like to find out what value of Y would be when X approaches 2.
As X approaches to 2, Y approaches to 4. Then we may claim that the
likelyhood of Y would be 4 when X = 2. If you claim anything else then
you have to prove it.

In the vase example, if we only look at the withdrawal portion of the
argument then the claim is not strong. If both putting in and taken
out of balls are taken into account. In order to prove that the vase
is empty at noon, you must have to show at certain time the rate of
taking out is greater than the rate of putting in.

.

Relevant Pages

  • 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: An uncountable countable set
    ... To become empty means there is a change of state in the vase, from having balls to not having balls. ... There are always a specific number of balls, if additions and removals occur instantaneously. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Since the vase was empty to start with, it cannot later "become" empty after once having been empty, at least according to that definition. ... Noon does not exist in the experiment, or else you have infinitely numbered balls. ... insertion or removal or location of balls is a function of time. ...
    (sci.math)
  • Re: infinity
    ... >>> Physically or mathematical it is not difficult to prove that the vase ... # of balls in the vase can be ... this statement alone is not sufficient to claim ... >>> the vase is empty before noon. ...
    (sci.math)
  • Re: infinity
    ... Number of balls in the vase at noon is f= OO. ... Unfortunately, if infinity gets involved, this statement alone is not sufficient to claim the vase is empty before noon. ... then the sum becomes 0. ...
    (sci.math)