I'd go ahead and call this one "stuff", except in fact I haven't.

[sniffnoy]

OK, how did I not know about this really nice proof of Minkowski's inequality before? (Answer: Because you don't know analysis very well, Harry.) A function ||•|| satisfying ||x||=0 iff x=0 and ||ax||=|a|||x|| is a norm iff its "closed unit ball" is convex. Checking this for the L^p norm is easy. Done. I mean, is that elegant or what? I'd only ever seen it proved via Hölder's inequality via Young's inequality.

Also: How the hell is S^-1Z[T] where S={T^m-1:m≥1}∪{T} (as mentioned in this MO question) a PID? Is it just me or is, e.g., (2,T^3+T+1) not principal? Maybe I should actually go look up the original paper.

Also, I need to learn how to use Axl's counters properly.

And stop reading LW so much. Eating up way too much time... I'm reminded of when I used to regularly check YKTTW...

-Harry

Comments

[joshuazelinsky.livejournal.com]

Re:LW, Have you read the recent discussions at LW about how much of what goes on there might be more "shiny rationality" than instrumental rationality?

Re:Minkowski, I must be missing something, how are you getting that that occurs iff the closed unit ball is convex?

[sniffnoy.livejournal.com]

Re:LW, Have you read the recent discussions at LW about how much of what goes on there might be more "shiny rationality" than instrumental rationality?

Yes, and I can't claim that wasn't an influence. :P

how are you getting that that occurs iff the closed unit ball is convex?

Oops! I seriously misstated that. Um. Well, here's the answer to what your question would mean had I written what I meant, and meanwhile I'll go fix the entry...

It goes, say you have ||x|| and ||y||, then we want ||x+y||/(||x||+||y||)≤1, i.e. ||(x+y)/(||x||+||y)||≤1, and (x+y)/(||x||+||y||) can be written as x/||x|| * ||x||/(||x||+||y||) + y/||y|| * ||y||/(||x+y||), closed unit ball convex so there you go.