@tb "I am not going to give more details here, since to flesh this out would be the topic of an advanced graduate course in arithmetic geometry, and I don't have time to write the notes for such a course!" :D
@JonasTeuwen ;D that's not so engineering. I took Hybrid Systems and Models of Systems' Design. I still don't how I managed. It's like @Asaf taking class in numerical methods
@JM It's getting harder and harder for me to believe that you're just a hobbyist. Afficionado would be a better term. And a damn versatile one at that!
If I'm having a conversation with an attractive woman at a party, inevitably a friend of mine will interrupt with a comment about how I like math. Party pooper.
@JM Yes, exactly. Hate those guys. Gave him verbally what amounted to a kick in the scrotum... Turned out to be the boss of the one throwing the party. Whoops.
After all my efforts trying to explain what an approximation algorithm is, "So what real-life problem do you solve?" I had to lie to him that we solve practical problems affecting airlines and such. I am sure some people do, but I don't.
@tb Well, I am not saying my Ph.D. is worthless. But I couldn't translate whatever I am doing into terms he can relate to -- I am guessing this is the usual trouble.
@Srivatsan If you look at the guy's activity page most of them are $\leq 10$ characters changed, the longer ones are hiding links using markdown and "edited title" means capitalization of the first word.
I just stated that $\binom{2n}{n}=(-4)^n\binom{-1/2}{n}$ follows by induction. I left out my derivation of that fact because I thought the rest was more pertinent, but I guess not since Mike had already given that part.
@robjohn It's your call. But it's somewhat sad for the wasted effort. Why not repost it in the other thread, explaining that you mistakenly posted it in the follow-up by Mike without seeing his answer? It is a slightly different take, I think.
@tb Well, now that I look at Mike Spivey's old answer more closely, it is pretty much the same as what I gave. I don't think it is really worth adding there. The only thing that I could add is the formula I stated a few messages back, which neither Mike nor I proved.
@robjohn Aw, that was nice. I would've told you, of course -- had I noticed it myself. I hadn't seen the first link myself since I assumed I knew what kind of proof Mike is talking about.
