If you let w be the first of the negation pairs, and q come before it. So the sequence goes …, q, w, -w, …
Then a plot of q (x axis) and w(y axis) looks like.
All points are within the orange line (which represents absolute(w)<-0.5*q+2.5 )
Note also that this graph appears approximately symmetric about the x axis. You can’t tell between …q,w,-w… and …q, -w, w, … The extra information about which item of the pair is positive resides elsewhere.
For comparison, the exact same graph, but using an unfiltered list of all points, looks like this.
Of course, many of the points outside the orange lines are the +- pairs, but not all of them. There are enough other points outside the orange lines that there is no way this is a coincidence that all the points in the top graph are within the lines.
If you let w be the first of the negation pairs, and q come before it. So the sequence goes …, q, w, -w, …
Then a plot of q (x axis) and w(y axis) looks like.
All points are within the orange line (which represents absolute(w)<-0.5*q+2.5 )
Note also that this graph appears approximately symmetric about the x axis. You can’t tell between …q,w,-w… and …q, -w, w, … The extra information about which item of the pair is positive resides elsewhere.
For comparison, the exact same graph, but using an unfiltered list of all points, looks like this.
Of course, many of the points outside the orange lines are the +- pairs, but not all of them. There are enough other points outside the orange lines that there is no way this is a coincidence that all the points in the top graph are within the lines.