Fortunados Problem or the Xless thansupgreater thannless than/supgreater than Conjecture and the Writing Notation (W)

Statement of the Problem Show that Xless thansupgreater thannless than/supgreater than is not equal to the written Xn. Also have an analysis to the closest Xn ≠ W (Xn). X=1 and n=.0∞1 is believed to be the closest. But what other relative analysis is there W is the writing notation. Let X be any number. Let n be any number. Examples, 01≠ 01 11≠ 11 1.5≠ 1.5 Also prove at what values of X and n will there be counterexamples.