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(Still confused.) Then it is possible to say, in principle, "for every combination of n out of the whole set of n, property(x) hold)" and mean ordered combinations? Is there any other meaning for "every 30 out of 30"?
(yes, it is probably because of my language background. I don't even use the Russian analogues all that often!)
It is possible to say that, but the work is being done by "combination." You can also say "for every permutation of n" and that means something different.
Typically when you say "for every x out of 30, property(x) holds" it means something like:
"every poster on lesswrong is a human being" (or more formally, "for every poster on lesswrong, that poster is a human being." (Note, this statement is meaningful but probably evaluates to false.)
Quantification is always over a set. If you are talking about permu... (read more)