Doubt on weights and pla

[Barath]

suppose i have a line f(x) = x , (for 2 dim) one side of which is +ve 1 and other side -ve 1..
Does this mean that target function is : [ -1 , 1] ? (since: -x + f(x) > 0 implies +ve 1 and -x + f(x) < 0 implies -ve 1)

and on running the PLA is the set of weights [-2 , 2] or any [-n, n] a valid solution for f(x) = x ? (since its just a constant to divide throughout?)

and when selecting random points, the PLA seems to run till infinity at times with
the same value of w repeating at regular intervals

am i getting the idea right here btw?