(a) Show that every nonempty subset of  that is bounded above has a largest element.(b) If...

(a) Show that every nonempty subset of  that is bounded above has a largest element.

(b) If , show there is exactly one  such that n<x<n + 1.

(c) If x − y > 1, show there is at least one  such that y<n<x.

(d) If y<x, show there is a rational number z such that y<z<x.