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What does "ordered sets" mean in this context? I had to sort them to get the desired result
There is no "ordered set" given, the statement speaks about "ordered pairs" which refers to the "2-component vectors (x,y)", and means that the order is important in (x,y), i.e., first component and second component have distinct meaning and can't be exchanged; in particular, (x,y) != (y,x) unless x=y.