Thinking out loud about the recursive Cantor function construction again. I realized shortly after the post that the points \(x = k/2^N\) do not become fixed points. On the other hand it seems right to focus on the plateaus where \(y = f_N(x) = k/2^N\)... the difficulty
I have sometimes liked to learn math from textbooks by doing all, or most, of the exercises. This can be really engaging when it is going well. A problem I have often run into is that I will get stuck. Sometimes talking about the problem unsticks it. Maybe writing about
An interesting thing about approximation is that it goes both ways. That is: If \(f(x)\) approximates \(g(x)\) under conditions \(Z\), then it's also true that \(g(x)\) approximates \(f(x)\) under conditions \(Z\). The most interesting example to me is approximating a discrete thing with a
From Hogfather by Terry Pratchett: "There's something wrong and he won't tell me?" said Susan. That made her even more angry. "But Albert is in on it, too," she added. She thought: Thousands, millions of years in the same job. Not a
Here is an interesting art project idea, free to whoever wants it: The John Smith group blog. You've heard of topical group blogs. This is just a group blog by people named John Smith. Preferably, all people named John Smith, but that might be a tall order; in