For a given irrational number α , y1,α=α. If yn−1,α is given, let yn,α be the first member of the sequence ({kα})k=1∞ to fall in the interval (0,yn−1,α) ({ x } denotes the fraction of the number x ). Show that there exists an open set G⊂(0,1) , which has a limit point 0 and for all irrational α , infinitely many members of the (yn,α) sequence do not belong to G. real analysisirrational number