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What do lowercase letters and letters in brackets mean? (In algorithms)
I mean things like L U L' U [L U2 L'] and (f R U R' U' f') U (F R U R' U' F')
 
Lower case letters can mean two things:

1) A wide turn (2 layers turned at once)
2) An inner-slice layer turn - like one of the two middle slices on a 4x4

You kind of have to know the context. In a 3x3 alg, there are no inner slice turns, just the middle slice, and it already has its own letter (M). So it's going to be a wide turn. In the alg you've shown, you'd be turning the front two layers together for the f and f' moves.

For brackets, those are "triggers". Essentially, these are really common sets of moves that show up in lots of algs. They are grouped together with brackets to aid with memorization. The idea is you see that set of moves and know "oh, that's a sexy move" rather than trying to memorize 4 more moves. So a simple alg becomes like "F [sexy move] F'" or something. Much easier to remember that way.
 
Also [r] can mean a cube rotation following R (Used in FMC Solutions) (it works with everything else also ie. [r'], [u2], etc...
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(Yes, it's allowed for FMC—it's in the regulations that you're supposed to read before attending a competition. This doesn't mean that it's a good idea to use this notation.)
 
Why? I’m thinking It might be because it looks like a move (last comp I had fmc used it and they counted it as moves but they changed it back )
Almost nobody uses the square bracket rotation notation; it's not something one would expect to see in a submitted FMC solution. If you use it instead of x/y/z, you're pretty much just making the grader's life harder. Also, if the grading is done by typing the solution into alg.cubing.net (or similar), it's worth noting that alg.cubing.net doesn't support this notation.
 
Oh thanks for letting me know. I will make sure not to use those at my next comp, the reason I used them at my last comp was because I wasn't confidante with xyz.
You actually should practise not using rotations at all for FMC; it makes everything simpler for everyone. (It's easier for you to check your solution to make sure you don't get a DNF; it's easier to start using intermediate/advanced FMC techniques like NISS and insertions; it's easier for the person checking your solution to check it.)
 
What do you consider a sub x solver?
Do you consider yourself a sub 20 solver when you get your first sub 20, when you manage to get a an avg of Y, when your global average is below 20, or when your average of last few hundred is below 20?
 
Do you consider yourself a sub 20 solver when you get your first sub 20, when you manage to get a an avg of Y, when your global average is below 20, or when your average of last few hundred is below 20?
I think that @Aerma does a great job explaining your question in this thread: https://www.speedsolving.com/forum/...20-from-the-cstimer-stats.70668/#post-1298499
Although the question from the other thread is a little different, the basis of the question is the same, so hopefully it helps.
 
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