The incompressibility method is an elementary yet powerful proof technique.
It has been used successfully in many areas (Li and Vitanyi, An Introducti
on to Kolmogorov Complexity and its Applications, Springer, New York, 1997)
. To further demonstrate its power and elegance we exhibit new simple proof
s using the incompressibility method. (C) 2000 Elsevier Science B.V. All ri
ghts reserved.