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aspera comments on On the importance of taking limits: Infinite Spheres of Utility - Less Wrong Discussion
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Great problem, thanks for mentioning it!
I think the answer to "how many balls did you put in the vase as T->\infty" and "How many balls have been destroyed as T->\infty" both have well defined answers. It's just a fallacy to assume that the "total number of balls in the vase as T->\infty" is equal to the difference between these quantities in their limits.