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RolfAndreassen comments on Open Thread, Jul. 27 - Aug 02, 2015 - Less Wrong Discussion
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There are different levels of impossible.
Imagine a universe with an infinite number of identical rooms, each of which contains a single human. Each room is numbered outside: 1, 2, 3, ...
The probability of you being in the first 100 rooms is 0 - if you ever have to make an expected utility calculation, you shouldn't even consider that chance. On the other hand, it is definitely possible in the sense that some people are in those first 100 rooms.
If you consider the probability of you being in room Q, this probability is also 0. However, it (intuitively) feels "more" impossible.
I don't really think this line of thought leads anywhere interesting, but it definitely violated my intuitions.
I opine that you are equivocating between "tends to zero as N tends to infinity" and "is zero". This is usually a very bad idea.