sunday 1

well, again today i'm trying to make math my focus. i finally just solved a problem that i wasn't able to figure out for a couple of days. the 'trick' i ended up using is a trick that i have thought of before in a similar context; in the end, the proof isn't very long! it's just a bit confusing because you have to do something sneaky, which is find some delta, and then cover your space with balls of radius delta/2 for everything to work out. but anyway, last night i entertained myself by making a big 25 minute mix of a bunch of good piano solos played one immediately after the other, with minimal audio editing things done in between to make it flow reasonably well... if i do enough math today to be satisfied i will probably try to make another such mix this evening. cardinals are playing right now, and losing by 1, but now a rain delay is starting... anyway, cardinals are coming to LA tomorrow to play the dodgers! no rain delays here, i would assume. in fact the weather has been perfect every day i've been here... anyway, plans for the rest of the day, other than math and music... well, all i know is that spaghetti dinner seems reasonably possible. well, that's all for now! thanks for reading! (oh by the way, if you're going to read the proof below, then there's one place where i put X where i should have put \chi, but it's pretty obvious what i meant and you might not even notice it...)