For a certain tolerance:
- one can not stop when the side of a square is the same size or smaller than the tolerance.
This is because the root is not finally found at the center of a certain square, but rather found at the center of a cluster of squares.
This is because of the imprecision of the root-test
Since the root is at the center of a cluster of squares the whole cluster, if the whole cluster can be bounded by a square with sides of tolerance length, any square in that cluster will be within tolerance of the real root