infinity

Hello everyone,

I'm having an argument with a friend about the following problem:

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?

An 2nd experiment goes as follows:
put no. 1 - 10 in, take no. 10 out, put no. 11-20 in, take no. 20 out, put
no. 21-30 in, take no. 30 out, etc.
(of course at the same moments as above)

My friend claims both experiments end up with an empty vase.
I think however the 2nd experiment ends up with a vase with an infinite
number of balls:
1-9, 11-19, 21-29 etc. are definitely in the vase.

He says it all has to do with Cantor's set theory, cardinality etc..., but
browsing the internet didn't really help me much.
Any information or relevant links are very welcome,

Thanks, Theo


.

Relevant Pages

  • Re: infinity
    ... > Suppose you have a giant vase and a bunch of ping pong balls with an ... > how many ping pong balls are in the vase? ... > My friend claims both experiments end up with an empty vase. ...
    (sci.math)
  • Re: infinity
    ... > Suppose you have a giant vase and a bunch of ping pong balls with an ... > how many ping pong balls are in the vase? ... Noon may be un-reachable in a physical sense, but this is not a physical ...
    (sci.math)
  • Re: infinity
    ... >> how many ping pong balls are in the vase? ... > bunch of blank ping pong balls, and put the numbers on them just before ... If on the first step, the Kilngon puts in the balls labelled wa', cha', ...
    (sci.math)
  • Re: infinity
    ... > how many ping pong balls are in the vase? ... bunch of blank ping pong balls, and put the numbers on them just before ... Klingon) will even notice that there are numbers on the balls. ...
    (sci.math)
  • Re: infinity
    ... problem is modeled in set theory ruled mathematics. ... > how many ping pong balls are in the vase? ... set.It is said to have cardinality aleph naught. ...
    (sci.math)
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