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Dec 22, 2022 at 16:34 comment added Terry Tao If the $E_n \cap [a,b]$ all contain a common point $x$, then the rounding $\tilde x$ of $x$ to the nearest integer multiple of $1/b^{3N}$ will lie in all of the $F_n$ for $N \leq n < 2N$.
Dec 22, 2022 at 13:57 comment added user44143 Was something accidentally negated here? How do we show that “$E_n\cap[a,b]$ have empty intersection almost surely” by showing that the intersection of nearby discrete sets are “empty with probability which goes to zero”?
Dec 22, 2022 at 5:13 history answered Terry Tao CC BY-SA 4.0