Show that if K (x) were computable, we could use the following procedure to create a short description for an incompressible string: function incompressible (n: integer) { for x ∈ {0, 1} n if K (x) > = n then output x }

K (x) = n

Explanation:

n is an integer, that is 0, 1 ...

K (x) = n, for x∈{0,1}

Hence, x∈ n

∴ K (x) = 0

and K (x) = 1

Then, K (x) = {0, 1, 2, 3, ... n}

For K (0) = 0

also, K (1) = 1

From the foregoing, the integers, 0,1,2 ... are sub-sets of x for every positive value of n.