The number x from [0,1] is written as an infinite decimal fraction. Having rearranged its first five digits after the point we can obtain another fraction that corresponds to the number x1. Having rearranged five digits of xk from (k+1)-th till (k+5)-th after the point we obtain the number xk+1. a) Prove that the sequence xi has limit. b) Can this limit be irrational if we have started with the rational number? c) Invent such a number, that always produces irrational numbers, no matter what digits were transposed. limitirrationalSequencealgebraDigits