 The proof uses a particular fact about computable real numbers.If "x" were computable then there would be a computable function "r"("n") such that |"q""j" - "q""i"| < 1/"n" for all "i","j" > "r"("n").To compute "r", compare the binary expansion of "x" with the binary expansion of "q""i" for larger and larger values of "i".