I was confonoted with the following problem today, and thought it was interesting enough to discuss it here:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

You have a box with balls numbered 1,2,3...n.

Suppose you began, by taking out balls numbered 1–100

and then put ball 1 back. Suppose you then removed balls 101–200

and put ball 2 back. Then you took balls 201–300 into your lap, found

ball 3, and put it back. And so forth. After doing this countably many

times, which balls are left in your lap?

2. Relevant equations

3. The attempt at a solution

I was tempted to affirm that, as there is a bijection between the number of balls that were put back to the box and the number of times you repeat this, f(n)=n, after n steps all balls would be inside the box . However, as there is also a function from N to the number of balls you have outside, namely f(x)=99x, I would conclude that you have the same number of balls inside and outside the box, in other words, the set of balls in the box and the one of balls outside it have the same cardinality.

Is this last conclusion correct?

I hope I was able to express myself clearly!

Thanks,

Daniel

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# Homework Help: Counting problem involving infinite

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