For those that just want the meat, this is about the Duffin-Schaeffer conjecture [0]. Here's the relevant paper: https://arxiv.org/abs/1907.04593 https://arxiv

For those that just want the meat, this is about the Duffin-Schaeffer conjecture [0]. Here's the relevant paper: https://arxiv.org/abs/1907.04593 https://arxiv.org/abs/1907.04593 For those that want a little more, the Duffin-Schaeffer conjecture is about rational approximations of real numbers. The setup is this: Given some real number, we're concerned with its rational approximations. To this we choose some function that assigns an "acceptable error" for every possible denominator. Thus, we want to look at the set of "acceptable approximations." A priori, we can intuit that if our errors are too strict, we might not have any---or only a handful---that meet our criteria. The Duffin-Schaeffer makes this intuition precise, giving a condition that tells us whether our set of acceptable approximations will be finite or infinite. [0]:https://en.wikipedia.org/wiki/Duffin-Schaeffer_conjecture https://en.wikipedia.org/wiki/Duffin-Schaeffer_conjecture