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Khoth comments on Probabilistic Löb theorem - Less Wrong Discussion
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Comments (39)
I wasn't summing a(n). It's the sequence a(n) that converges, not its sum, and the partial products of the b(n) are equal to the a(n), not the partial sums of the a(n).
Certainly an infinite product of 0<n<1 can't be one. Nobody's disputing that.
Oh, then it sounds like we are in perfect agreement that my initial claim was wrong; however, we can now generate an infinite series of probabilities less than one whose product remains higher than 1-epsilon for any epsilon. If 1-epsilon is used as the determinator of what the system proves true, Löb's theorem holds.