= 27d567bc2d48d9f40e9ccc20ea370b15)
Stuart_Armstrong comments on Probabilistic Löb theorem - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (39)
(1-a)(1-b) = 1-a-b+ab > 1-a-b.
Hence P(A) > (1-a)(1-b) implies P(A) > (1-a-b). Since I let these quantities get arbitrarily close to zero, the quadratic difference term doesn't matter.
P(A) ≥ (1-a)(1-b) U (a,b)>0 implies P(A) > (1-a-b). That's a (very slightly) stronger form. I noticed what I thought was an error where you were adding improbabilities together instead of multiplying.
The proof doesn't need the stronger form, however.