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1. How do you compare sequences in L infinity? Having a bounded sequence there implies that L infinity is totally ordered, which means there has to be a way to do that...
2. I had to look that theorem up, and funnily enough, I found proof of what you asked: http://en.wikipedia.org/wiki/Bolzano-Weierstrass

3. Maybe for a day or so. But no guarantees!
4. LOLOL, nice one
5. The description was also in Russian which I can almost fluently read . We have some guitars in my school where I really started learning and someone recently dropped a hollow wood electric guitar, similar to this model http://images.guitarcenter.com/produ...32365026_A.jpg. We had to have a contest over who gets to use it earlier in the year and I won by 2 votes (we had to see who sounded best on it and then voted). The other guitars are all acoustic and a few other various electrics.
6. I do play the guitar, both electric and acoustic. I've been doing it for about 1 year now.
7. oh yes I remember you sending me that video before , it really is incredible how fast you manage to play . I've never actually really looked into the MotM thread
8. Basically solving the bottom layer edges so that you are solving them in the right position next to the other edge colors, but not necessarily in regards to them matching up with center colors. Then rotating the bottom at the end to line them up with the correct centers. Kind of hard to explain, haha, I'd suggest looking it up.

And yeah, I believe there are 21 PLLs. Man, I hated memorizing the g-perms. They don't flow at all, it seems.
9. My best is 28.55 seconds. Sadly, I've become out of practice with a 3x3x3 since mine is really trashy. Whenever I get a new one I will try to get much better.

At my peak, I knew advanced cross, intermediate F2L, all the PLLs, and all but 7 OLLs.
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