Math Tidbits

Maximal FencesI got nerd sniped by this video and with some help from my friend Claude was able to optimize some of the existing records and set some new ones.1Infinite TetrationThere are a bunch of videos talking about how the infinite tetration function is only defined in a specific range and strangely only hits finite values at the ends of the range, but they don’t show what it actually looks like as a function, so here it is:Thanks for reading Bram’s Thoughts! Subscribe for free to receive new posts and support my work.You might wonder what’s going on at the end points here. On the right it’s going completely vertical. There’s nothing actually funny happening on the left, that’s just where the formula for it using the W function splits into two value. But we can make an analytic continuation of it like so:2Since we’re defining tetration we can make the rules and there’s no reason to limit it to the happenstance constraints of W. But this still leaves the question of what’s going…